TimboMull: it doesn't give me any other option BUT to continue the game I've saved - as opposed to trying other in-game options, like a quick one-holer with someone.
I think it can be tricky.. sometimes you can continue a game on the opposite platform and other times you can not because the two platforms offer different types of game options.
For example you could start and save an uneven lies round on Desktop but it would not allow you to play that round on the mobile platform, I do not believe.
The same would go for blitzes, skins, AS and multi player type games because you can not play cross platforms... Now some desktop players have loaded an mobile app emulator program thus allowing them to play on the mobile platform, but they can no longer play multiplayer games with other desktop players until they go back to their desktop game client.
I am not sure if that is what you are getting at, but there are compatibility issues that can explain some of the things I believe you are observing...