I suspect the bulk of the discrepancy arises from your move analysis depth settings, specifically the Full Analysis Depth and Self Analysis Depth. When you select “show lines,” the Self Analysis Depth setting governs the browser engine’s search depth for the additional displayed lines. Whereas, the Full Analysis Depth is relevant when running the full game report on the server. If those search depth settings are different, different move recommendations are possible, since the higher depth analysis will be more accurate.
Incidentally, the analysis depth of 15 presented in your screenshots is really low.

Hello, I'm new here and I try to understand how the chess engine work ? Can someone explain to me, please ? I was analyzing my game and the engine showed that cxd4 as a best move. After I did the move the engine saw this move as an excellent one but the best move it was c4. How come ? I don't understand this. Thanks.