I literally just had a thread open with this same question.
To quote @Martin_Stahl from that forum:
They run at different depths and depending on the app version may also run on different back end versions of that code
Different analysis on phone vs app
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May 10, 2023
0
#3
Besides the depth one also has to consider...is the same version of Stockfish being used?
May 20, 2023
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#4
They use a version most adequate for the processor speed and memory available. On lichess you can see that more clearly, the depth & SF version (often some "hand-crafted" versions specifically designed for this or that purpose) are clearly displayed next to the button where you switch on and off the engine. It varies very much. Also, e.g. when you play against bots, or when you play drills against the computer, they are not just different "strengths"(depth) of the same engine but the version may vary.
(But you can to some extend make a different choice in the "settings" and maybe get the same engine, depth & same result, probably with a longer "thinking time" on the smartphone compared to the computer.)
But wait.... I think this is true for the "analysis" that is made on your device, but not for the "game report" which is computed by the c.c server. (You can notice that you can't get a game report in offline mode.) But here also they use different versions of the server software. Onec I noticed that next to (or instead) the "depth = ..." information usually displayed when it makes the game report, it displayed "fast mode" or similar when I checked a game review during a tournament (blitz arena). And it was indeed significantly faster (the blue line turned around the square only once or twice, not 10 times as usual when you request a game review.
BTW, I think that ("computing training plan" and similar blabla it displays) is totally "fake" and does not correspond to what the server really does and/or the time required for it, but it is just made to reduce server load by slowing down the frequency of user requests.
When I analyze a chess game on the chess.com app, it shows different results than when I use the website. For example, on the app it said I had 69% accuracy in a game, but in the website it said I had 74% accuracy in the same game. Why is this?