On this website, brilliant moves are always a piece sacrifice, whether by directly putting a piece in harm's way or allowing one that's being attacked to be lost. In actual OTB games, this is usually the case as well, especially because the standards are much higher.
A pawn sacrifice pretty much never gets a brilliant. However, moving a pawn when another piece is under attack can be brilliant.
Brilliant moves on chess.com seemingly require that you have a piece of some kind under threat with the move (while the move you make is also one of the best moves available).
This can, of course, be a direct sacrifice that forces your opponent to capture. However, there's also a concept of a "poisoned piece" that can be a brilliant move that Fr3nchToast alluded to by making a move that puts your piece (or leaves another of your pieces) in harm's way. In this case, it isn't a capture that the opponent is forced to make, but if the opponent does capture it, the position will get substantially worse for them (e.g. because it deflects a crucial defending piece away or disregards a powerful attack you've set up).
I once had a debate on TikTok about what a brilliant move in chess is. Some said that a brilliant move always means the opponent will be checkmated, whether it's because of sacrificing the queen, knight, bishop, or rook.
Then I commented that a brilliant move doesn't always have to involve a sacrifice, but it's more about gaining a superior position after the sacrifice.
Then someone else commented, "Is there such a thing as a brilliant move without a sacrifice?"
That's when I started thinking, do we have to make a "sacrifice" if we want to get a brilliant move? Even if the sacrifice is only using a pawn?
Yesterday I made a sacrifice with my queen, but it turned out not to be a brilliant move. Then I posted it on a forum and the responses varied, but one thing was for sure, my move was "easily predictable".
https://www.chess.com/forum/view/general/i-sacrified-my-queen-but-didnt-get-brilliant