The "best move" definition by the same engine explicitly says "The chess engine's top choice". If the move was exactly what the engine proposed in the first place, it wouldn't be a Brilliant move. That's the reason why after a while the engine corrects every brilliant move into a best, since, it now picks that move instead. A brilliant move is literally a move that wasn't even considered in the first place but turned out to be even better than the best. (And after a while, it will be considered just best)
(The engine is continously being trained by our plays)
Oof, true enough. I'd saved the game containing my first brilliant move to my library, but now it shows as no longer brilliant. I guess I won't check on my other brilliant moves to preserve what illusion is left.
A bralliant move is basically a move that goes deeper then the engine's depth. Such as 35 move checkmate, when the engine can only see twenty moves ahead.