Salamalaikum, could you please give a layperson like me an understanding of how the hadiths are classed. I see terms like sahih for Bukhari and Muslim, but then there are others that are also considered sahih but are not listed in Bukhari and Muslim. What is hasan? what is daeef(sp?)? and who determines the lesser known hadiths are sahih or hasan? Is that a majority opinion? Jazakallah khairun
Alaikumassalam wa rahmatullah,
Sahih al-Bukhari and Muslim are simply two handbooks written for legal scholars. They bring together authentic hadiths that are useful for a legal scholar to know. They are not meant to be complete encyclopedias of hadith. All hadith scholars are qualified to determine the authenticity of hadiths. Al-Bukhari and Muslim are just better known than the others. Each hadith scholar can make their own sahih collection, for example there is Sahih Ibn Hibban.
The word ṣaḥīḥ refers to a hadith that has a good enough quality (text and chain of narrators) to be considered very likely to be truly from the Prophet 
.
The word ḥasan refers to a hadith that is not good enough to be considered ṣaḥīḥ (it may have some half-trustworthy transmitters), but it is considered good enough to be considered possibly authentic.
A ḍaʿīf (”weak”) hadith is one that comes from untrustworthy transmitters so it is considered likely to be false/fabricated.