Basic difference in the knowledge of Sayyidna Musa (AS) and al-Khadir (AS): Resolution of an apparent dichotomy
Naturally, a question arises here. We see that, according to the explanation of al-Khadir (AS), the nature of the knowledge given to him was different from that of the knowledge of Sayyidna Musa (AS). Now, when both these two areas of knowledge were given by Allah Ta'ala alone, why did this contradiction and difference show up in their two respective injunctions? Qadi Thanaullah of Panipat has given a research-based answer to this question in his Tafsir Mazhari. It is the closest to being right and appealing. Given below is a gist of what I understand from his presentation:
'The blessed souls Allah Ta'ala honors with His revelation and prophet-hood are generally those who are entrusted with the mission of making people better. Sent to them is a Book and Shari'ah which offer principles and rules that serve as blueprints of guidance and betterment for the creation of Allah. Blessed prophets and messengers mentioned in the noble Qur'an as such were all assigned with the mission of Law and Reform. To this related the Revelation they received. But then, there are services essential to the realm of creation (takwin) as well. Generally, appointed to take care of these are the angels of Allah. However, Allah Ta'ala has specifically chosen some from among the group of prophets also in order to carry out the services of takwin (whereby the decisions of Allah's will relating to the managment of His creation are enforced). Al-Khadir (AS) belongs to this very group. These imperatives of takwin relate to minor incidents and events, that a certain person should be saved from getting drowned, or someone should be killed, promoted or demoted or subdued. These matters do not relate to common people at all, nor are they addressed by these imperatives. In such events of minor consequences, one may confront some of those situations where killing a person is against the religious law. But, under the imperative of creation, that particular event has been exempted from the general religious law and the act has been made permissible for the person who has been appointed to carry out this imperative of takwin. Under such conditions, the experts of religious law are not aware of this exempted injunction and are compelled to call it 'haram (unlawful) and the person who has been exempted from this law under the imperative of takwin remains in the right in his own place.
In short, wherever such a contradiction is perceived, it is no contradiction in the real sense. It is simply the exemption of some minor events from the general religious law. In al-Bahr al-Muhit, Abu Hayyan said:
ألجمهور على أن الخضر نبي و كان علمه معرفة بواطن قد أوحيت إليه و علم موسى أحكام والفتيا بالظاهر
The majority holds Al-Khadir (AS) to be a prophet and his knowledge was the gnosis of (the inner dimensions of the human) self which was revealed to him and the knowledge of Musa (AS) was of the injunctions and rulings on the apparent. (Al-Bahr al-Muhit, p. 147, v. 6)
For the aforesaid reason, it is also necessary that this exemption should take effect through revelation to a prophet. The Kashf (illumination) and Ilham (inspiration) of some Waliyy (man of Allah) are never sufficient to make such an exemption effective. This is the reason why the act of al-Khadir (AS) in killing a boy apparently without a just reason was haram (unlawful) in the sight of the Shari'ah which rules on the apparent. But, as for al-Khadir (AS), he was appointed to do that while exempted from this law as an imperative of creation (takwin). Taking the Kashf and Ilham of some non-prophet on the analogy of al-Khadir (AS) and thereby taking something haram (unlawful) to be halal (lawful) - as popular among some ignorant Sufis - is totally anti-religion and certainly, a rebellion against Islam.
Ibn Abi Shaibah reports an event relating to Sayyidna Ibn 'Abbas (AS) by saying that Najdah Haruri (a Kharijite) wrote a letter to Sayyidna Ibn 'Abbas and asked as to how did al-Khadir (AS) kill a minor boy when the Holy Prophet (Sallallahu Alaihi Wasallam) has prohibited the killing of minors. Sayyidna Ibn 'Abbas answered his letter by saying, 'if you were to receive the same knowledge about some minor as was received by Sayyidna Musa's 'man of knowledge' (that is, al-Khadir AS), the killing of a minor would become permissible for you too!' What he meant was that al-Khadir (AS) had received his knowledge about it only through revelation exclusive to a prophet. That nobody can have now because prophet-hood has ended. There is to be no prophet after the Last among Prophets, that is, Muhammad al-Mustafa (Sallallahu Alaihi Wasallam), who could have through revelation knowledge about some particular person to have been exempted under Divine command in the case of such events. (Mazhari)
From this event too, the real thing becomes clear, that is, no one other than a revelation-receiving prophet has the right to declare anyone as exempted from any Islamic legal injunction.

باب مَنْ سَأَلَ وَهْوَ قَائِمٌ عَالِمًا جَالِسًا .
Chapter 45 : That who asked while standing to a religious scholar who was sitting.

Purpose of Tarjamatul Baab
In general Islam does not like that people having some rank or social status, should sit and make others to stand around them. This bespeaks of arrogance which Islam does not like. By establishing this title for this chapter Imam Bukhari wants to convey that at times of need, for example, when the questioner is in hurry he can ask questions while standing when the learned scholar is sitting.

Hadith No. 122
حَدَّثَنَا عُثْمَانُ قَالَ أَخْبَرَنَا جَرِيرٌ عَنْ مَنْصُورٍ عَنْ أَبِى وَائِلٍ عَنْ أَبِى مُوسَى قَالَ جَاءَ رَجُلٌ إِلَى النَّبِىِّ - صلى الله عليه وسلم - فَقَالَ يَا رَسُولَ اللَّهِ ، مَا الْقِتَالُ فِى سَبِيلِ اللَّهِ فَإِنَّ أَحَدَنَا يُقَاتِلُ غَضَبًا ، وَيُقَاتِلُ حَمِيَّةً . فَرَفَعَ إِلَيْهِ رَأْسَهُ - قَالَ وَمَا رَفَعَ إِلَيْهِ رَأْسَهُ إِلاَّ أَنَّهُ كَانَ قَائِمًا - فَقَالَ مَنْ قَاتَلَ لِتَكُونَ كَلِمَةُ اللَّهِ هِىَ الْعُلْيَا فَهُوَ فِى سَبِيلِ اللَّهِ عَزَّ وَجَلَّ

Narrated Abu Musa (RA)
A man came to the Prophet and asked, "O Allah's Apostle! What kind of fighting is in Allah's cause? (I ask this), for some of us fight because of being enraged and angry and some for the sake of his pride and haughtiness." The Prophet raised his head (as the questioner was standing) and said, "He who fights so that Allah's Word (Islam) should be superior, then he fights in Allah's cause."

Comments
Once a person came to Rasulullah (Sallallahu Alaihi Wasallam) and asked him a question while standing when Rasulullah (Sallallahu Alaihi Wasallam) was sitting, as is evident from the statement of the narrator that he (Sallallahu Alaihi Wasallam) raised his head in order to see towards the questioner. His question was as to which fighting will be considered in the way of Allah as people fight for many reasons like with anger or for family or national pride. Rasulullah (Sallallahu Alaihi Wasallam) gave him a brief and comprehensive answer, he said, that fighting alone will be considered in the way of Allah which is meant to make the word of Allah superior and dominant in the world.
باب السُّؤَالِ وَالْفُتْيَا عِنْدَ رَمْىِ الْجِمَارِ
Chapter 46 : To ask and give a juristic view (at Mina during Haj) during Rami Jamaar (while throwing pebbles at Shaitaan))

Purpose of Tarjamatul Baab
Imam Bukhari (RA) wants to set guidelines regarding the asking of questions during busy time. Rami Jamaar is a time when every Haj pilgrim is extremely busy. If a learned scholar is asked questions during this time, should he answer or not?

Hadith No. 123
حَدَّثَنَا أَبُو نُعَيْمٍ قَالَ حَدَّثَنَا عَبْدُ الْعَزِيزِ بْنُ أَبِى سَلَمَةَ عَنِ الزُّهْرِىِّ عَنْ عِيسَى بْنِ طَلْحَةَ عَنْ عَبْدِ اللَّهِ بْنِ عَمْرٍو قَالَ رَأَيْتُ النَّبِىَّ - صلى الله عليه وسلم - عِنْدَ الْجَمْرَةِ وَهُوَ يُسْأَلُ ، فَقَالَ رَجُلٌ يَا رَسُولَ اللَّهِ نَحَرْتُ قَبْلَ أَنْ أَرْمِىَ . قَالَ ارْمِ وَلاَ حَرَجَ . قَالَ آخَرُ يَا رَسُولَ اللَّهِ حَلَقْتُ قَبْلَ أَنْ أَنْحَرَ . قَالَ انْحَرْ وَلاَ حَرَجَ . فَمَا سُئِلَ عَنْ شَىْءٍ قُدِّمَ وَلاَ أُخِّرَ إِلاَّ قَالَ افْعَلْ وَلاَ حَرَجَ .

Narrated 'Abdullah bin 'Amar (RA)
I saw the Prophet near the Jamra and the people were asking him questions (about religious problems). A man asked, "O Allah's Apostle! I have slaughtered the Hadi (animal) before doing the Rami." The Prophet replied, "Do the Rami (now) and there is no harm." Another person asked, "O Allah's Apostle! I got my head shaved before slaughtering the animal." The Prophet replied, "Do the slaughtering (now) and there is no harm." So on that day, when the Prophet was asked about anything as regards the ceremonies of Hajj performed before or after its due time his reply was, "Do it (now) and there is no harm."

Comments
This Hadith has been quoted in previous chapters as well.

باب قَوْلِ اللَّهِ تَعَالَى ( وَمَا أُوتِيتُمْ مِنَ الْعِلْمِ إِلاَّ قَلِيلاً )
Chapter 47 : The Saying of Allah "And of knowledge you (mankind) have been given only a little". (17:85)
Purpose of Tarjamatul Baab
Allah Ta'ala says that all of you have been given very little knowledge as compared to the knowledge of Allah. So, neither the questioner should hesitate to ask the question nor the scholar should avoid to answer if he knows the answer, particularly if the question is related to some important issue.

Hadith No. 124
حَدَّثَنَا قَيْسُ بْنُ حَفْصٍ قَالَ حَدَّثَنَا عَبْدُ الْوَاحِدِ قَالَ حَدَّثَنَا الأَعْمَشُ سُلَيْمَانُ عَنْ إِبْرَاهِيمَ عَنْ عَلْقَمَةَ عَنْ عَبْدِ اللَّهِ قَالَ بَيْنَا أَنَا أَمْشِى مَعَ النَّبِىِّ - صلى الله عليه وسلم - فِى خَرِبِ الْمَدِينَةِ ، وَهُوَ يَتَوَكَّأُ عَلَى عَسِيبٍ مَعَهُ ، فَمَرَّ بِنَفَرٍ مِنَ الْيَهُودِ ، فَقَالَ بَعْضُهُمْ لِبَعْضٍ سَلُوهُ عَنِ الرُّوحِ . وَقَالَ بَعْضُهُمْ لاَ تَسْأَلُوهُ لاَ يَجِىءُ فِيهِ بِشَىْءٍ تَكْرَهُونَهُ . فَقَالَ بَعْضُهُمْ لَنَسْأَلَنَّهُ . فَقَامَ رَجُلٌ مِنْهُمْ فَقَالَ يَا أَبَا الْقَاسِمِ ، مَا الرُّوحُ فَسَكَتَ . فَقُلْتُ إِنَّهُ يُوحَى إِلَيْهِ . فَقُمْتُ ، فَلَمَّا انْجَلَى عَنْهُ ، قَالَ ( وَيَسْأَلُونَكَ عَنِ الرُّوحِ قُلِ الرُّوحُ مِنْ أَمْرِ رَبِّى وَمَا أُوتُوا مِنَ الْعِلْمِ إِلاَّ قَلِيلاً ) . قَالَ الأَعْمَشُ هَكَذَا فِى قِرَاءَتِنَا .

Narrated 'Abdullah (RA)
While I was going with the Prophet through the ruins of Madina and he was reclining on a date-palm leaf stalk, some Jews passed by. Some of them said to the others: Ask him (the Prophet) about the spirit. Some of them said that they should not ask him that question as he might give a reply which would displease them. But some of them insisted on asking, and so one of them stood up and asked, "O Aba-l-Qasim ! What is the spirit?" The Prophet remained quiet. I thought he was being inspired Divinely. So I stayed till that state of the Prophet (while being inspired) was over. The Prophet then said, "And they ask you (O Muhammad) concerning the spirit --Say: The spirit -- its knowledge is with my Lord. And of knowledge you (mankind) have been given only a little)." (17.85)

Comments
Some Jews tried to tease Rasulullah (Sallallahu Alaihi Wasallam) and asked him about the soul (Rooh). Allah Ta'ala sent His inspiration to him in which he was told to tell those questioners that the whole knowledge which the creation possesses is very little as compared to the knowledge of Allah who is All-Knowing. The soul (Rooh) is from the word of Allah (Aalam-i-Amr).

What is عالم أمر) Aalam-i-Amr?)
Scholars are of different opinion regarding the nature of Aalam-i-Amr. Some say that the visible world is Aalam-i-Amr while some say that the visible world is Aalam-i-Khalq and the invisible one is Aalam-i-Amr. Mujaddid Alaf-i-Thani (RA) says that Aalam-i-Khalq is below the throne (Arsh) and Aalam-i-Amr is above the throne. Sheikh Akbar (RA) says that all materialistic things belong to Aalam-i-Khalq and all non-materialistic things which Allah created with the word كن i.e., ‘Be' belong to Aalam-i-Amr. The Soul is also non-materialistic which has been created with the word كن.

باب مَنْ تَرَكَ بَعْضَ الاِخْتِيَارِ مَخَافَةَ أَنْ يَقْصُرَ فَهْمُ بَعْضِ النَّاسِ عَنْهُ فَيَقَعُوا فِى أَشَدَّ مِنْهُ
Chapter 48 : That one who left some of his powers fearing that some people may not understand them and may get involved in greater misunderstanding.

Purpose of Tarjamatul Baab
In previous chapter it was said that people have little knowledge. In this chapter it is being said that one should refrain from saying such things to people which they may not understand but instead may get more confused and misled.