Let me just clarify so you don’t get confused:
Most Stringent to Least Stringent:
Beis Yosef Glatt- required for Sephardim; NO ADHENSIONS IN THE LUNG AT ALL
Ashkenazic Glatt-stringecy for Ashkenazim; There are up to two easily removable adhensions (called “rir”)
Non-glatt–only for Ashkenazim; Some adhensions that are tested to see if they are problematic