What exactly are the conditions of al-Bukhari and Muslim?

I've noticed that this question has never been asked before even if we have posts such as: https://islam.stackexchange.com/questions/23/what-are-the-requirements-of-a-sahih-hadith https://islam.stackexchange.com/questions/23212/which-criteria-the-rawisarabic-narrators-of-sahih-hadith-had-to-fulfil I've tried to address this topic before in my answer on https://islam.stackexchange.com/questions/7864/what-are-the-terms-of-that-which-has-reached-tawatur , however I didn't mention what exactly these conditions are, even if I have a hint of an answer about it, at least for one of the related partial questions which I want to have answers. And here I quote the partial question which I'd like to have answered: So what exactly is the condition of al-Bukhari (is it solely related -as-sanad- to the narrator chain or also to the content al-matn- of a hadith)? and what is the condition of Muslim? What is the difference between both conditions?