My understanding is that a great move (!) is the only correct move in a critical position, whereas a brilliant move (!!) is like some super hard to find move that wins the game. Is this correct?
yes
chess.com is good, however, they aren't perfect, so they really can't find the difference sometimes.
If you mean here, brilliant moves are sacrifices that are best or good, influenced some by rating.
Brilliant moves require sacrifice and aren't the only move that works necessarily but they can be great moves with sacrifice. It has to be a sacrifice where you get no immediate material compensation.
My understanding is that a great move (!) is the only correct move in a critical position, whereas a brilliant move (!!) is like some super hard to find move that wins the game. Is this correct?