All of them are a joke, download the PGN and run your game in an actual computer.
Deep vs Maximum Analysis

Then you are busted brah.
If you want to get a good analysis enter to chess.com with your computer and downlod the PGN of your game, then run it with Stockfish.
I guess you could also do the same with a tablet, maybe the app has the option of downloading PGNs.

I am also considering starting a premium membership - and want to know the difference between the Deep (gold level) and Max (Diamond level) analysis.
Please respond

I agree with BronsteinPawn. The analysis available is very flawed often, not always. I get the PGN when I am serious and run it on Fritz with the Komodo engine.

The Max. at chess.com is a quick look. I often get different results by downloading the pgn file, loading it into the freeware Lucas Chess, then having built-in Stockfish 8 do a 20-ply analysis, which takes about 70 seconds per half-move on my quad-core, 3.2 GHz laptop. While i'm doing something else.
Hello paying members. I'm thinking I might join you in your support of chess.com. I enjoy the tactic trainer in this app and the game analysis function. So. My over worded question is... what is the difference between Deep vs Maximum Analysis?
Much appreciation,
Kingpawnofwar