The difference is in sentences formed around them, but the meaning is pretty much the same. Person A: Have you found your pen YET? Person B: No, I haven't found it YET. (No, I still need to look for it) Person A: Have you found your pen YET? Person B: No, NOT YET. (No, I still need to look for it) Person A: Where is your pen? Person B: We are YET to find out. (I don't know but hopefully, we will find it soon and find out where it was) Are we there YET? (Have we arrived to the destination or we need to travel more?)

A native English speaker would only say 'not yet' in answer to a question, or when explaining that something has not happened yet. "the best part is not yet to come' = nonsense. 'the best part is yet to come" - correct

Yet -It is about to happen soon but you can't exactly tell when. -Example: The best part is yet to come. Not Yet - You have been in the situation before and can tell when it is about to happen. -Example: The best part is not yet to come.