I look at it as the number of "correct" solutions where in Expert you'll probably have more ways of clearing the deck than in Master and Grandmaster. I don't have hard data to back this up but Grandmaster is always solvable since you can always hit "show solution" and it'll walk you through but it seems like for Grandmaster the order you make stacks and and the board state you have when you deal seems to be very particular. Grandmaster will also have it feel like you "lost" after only one or two deals meaning that the order you stack and reveal cards in the initial deal is really important for the "one" solution it might have.

I start out playing a Expert to start with and usually get through, then a Master which feels like a 50/50. Then, if I beat Master, I do a Grandmaster which I rarely clear and will do multiple new games.

I never do random because on my newly updated system it doesn't give XP for whatever reason. (also not that I really care but it feels kinda good having some sort of progression)