I have read Copts claim to be the direct descendents of Ancient Egyptians, but I've also read things written by people that they are actually descendents or leftovers from the Greek or Roman period of Egypt.
Who exactly are the Copts and who were their ancestors? Do they share the same ancestors as Egyptian Arab-Muslims?
This isn't 'scientific' but just based on physical appearance I find the Copts look quite Mediterranean and don't look much different from the Lebanese or Greeks, while Egyptian Arab-Muslims look different from Egyptian Copts and are a lot darker.
I can't speak for their genetics, but the Coptic language is a direct descendant of Ancient Egyptian, albeit written in a Greek script. Since the Copts did not originate as an ethnoreligious group but rather morphed into one over time, it's most likely that the Coptic community is descended from early Christians of both ethnic Egyptian and ethnic Greek descent. The only major ancestral distinction between the majority of Egyptians and the Copts would be lesser degree of interbreeding with the Arabians who immigrated following the rise of Islam.