They both mean "most" (I think?) so what's the difference between them? Are they interchangeable?
Yes, they both mean "most" and are almost interchangeable. But sometimes 제일第一 can be used as a noun, meaning "the best", while 가장(pure korean) is never used as a noun. There is a different word 가장家長 which is a noun, but it has completely different meaning.
One note, "가장" can also be a noun, just a different meaning (a person who is leading the family; husband). However, I know that that's not what Kasturi Mone asked for. Jul 25, 2020 at 20:31
@David Lee Well, I already mentioned that in my answer, probably you didn't read the last line? Also, there are yet another word 가장假裝, which means "to pretend (to be someone else/to have certain authority)" this is almost always used as a verb 가장하다.– AbsolJul 27, 2020 at 2:15
My bad, should have read your answer more carefully. Jul 27, 2020 at 5:03