the Fatwa Department Research Committee - chaired by Sheikh `Abd al-Wahhâb al-Turayrî
The conditions of authenticity that both al-Bukhârî and Muslim relied upon in their Sahîh compilations can be briefly summarized as follows:
1. All of the narrators in the chain of transmission must be reliable.
2. The chain of transmission must be unbroken.
3. The hadîth had to be free from hidden defects and had to not conflict with other stronger or more numerous narrations.
The main difference between al-Bukhârî and Muslim is with respect to a type of hadîth known as mu`an`an. This is a hadîth whose chain of transmission contains the Arabic word “`an”. This word can be translated in this context as “on the authority of”.
The problem with it is that it does not imply that you actually heard the statement directly from the person. If you say “`an Ahmad”, this means that you are attributing some statement to Ahmad, but it does not mean that you necessarily heard the statement directly from him. This means that when the word “`an” appears in the chain of transmission, there is a chance that there is a gap in the chain.
According to al-Bukhârî, a hadîth that is mu`an`an could not be considered to have an unbroken chain of transmission unless there is proof that both the narrator and the person from whom he is narrating actually met at least once.
According to Muslim, it is enough that he two narrators in question lived at the same time and could have met.
Source: Islam Today