Best move is better than excellent move. Though, there is a brilliant move (I never got it in any of my games ) which is better than best move. The way I understand it, brilliant move is assessed as better than "best" move after it is played. It probably has something to do with the depth in which you conclude the analysis, though I am really not sure how it is determined as brilliant precisely.
Best move vs Excellent
Don't get too stuck up on that, it is Just computer terminology, doesn't matter If You made a book, best, excellent or brilliant move, in the end it just means that You played the first or second best move according to the computer. What's more important, rather than being amazed by one's own moves, Is to analyse mistakes and blunders I order to make real progress. Indeed, even a 600 elo guy can make a brilliant move, but It means nothing, the following 15 blunders played are what Is Important.
In my understanding, an excellent move must be better than best move but the frase "Best move" must be by definition the best move, even better than excellent. Which is it????
The analysis is complete bollox. If you take the time to actually analyze your game on your own or with engine assistance you will find moves that are called inaccurate, good, or even blunder when your analysis concludes that it was the best move. Conversely, you will see moves called best that turn out to be stinkers upon further analysis. Also, engines are dumb and have no concept of strategy (except maybe Alpha Zero and Leela) I wouldn't even use the feature to be completely honest with you, it's a waste of time.
Best move, by definition, is the BEST. Nothing can be better than Best. (Remember the phrase: good, better, best.) So best would be better than excellent, and I think better than Brilliant. You should be able to tell by looking at the overall "score" shown for the actual move and the suggested move (if the best move was not made).
There is one caveat, however, and that is the "depth" to which the analysis has gone. Often, at a "shallow" depth, say 10, moves will differ from a "deeper" one at 20 and maybe even deeper at 30.
Btw, that's not "engine terminology" or "computer terminology" in a general sense. It's just some proprietary language chess.com made up.
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Do you have any reference to this specific terminology being used elsewhere?
In my understanding, an excellent move must be better than best move but the frase "Best move" must be by definition the best move, even better than excellent. Which is it????