I often read Ahadith from sunnah.com. On the website, the ahadith in the Sahah Sitta, except Bukhari and Muslim, are classified as Sahih, Hasan or Da'if with either Al-Albani or Dar-us-Salam in the parentheses.

Can you please give me a brief idea of the criteria of these two for classifying ahadith. I am someone who trusts Bukhari and Muslim, and I generally trust the opinions of scholars when they classify a hadith in the remaining Sahah Sitta as Da'if. But since a lot of ahadith in the remaining four are classified as Da'if on sunnah.com, I am beginning to wonder what their criteria is.
In short, should I accept what they classify as Da'if to be Da'if? I do not have any problem with their classification as Sahih or Hasan.

Thank you.