It's a sort of infinite demo, where you have all of the multiplayer functionality, but two submarines to choose from in the free version. You also get two out of 7 missions in the free version with 3 difficulties each (granted, even in the full version, you need to do well in the existing missions to unlock the rest). There's also a limitation on crew of some kind, but with only two submarines in the free version of 1 or 2 crew each, this shouldn't be much of an issue. Similarly, there's also apparently some kind of limit on the camouflage options you get, but in the entire day that I had spent playing the free version nearly nonstop, I never encountered said limit.
Even when you get the premium version (a 10 USD unlock), if that's the first thing you do before even playing the game, you will still only have that one free starting submarine until you play in the single player or multiplayer modes enough to unlock the other roughly 20 submarines.
If you advance to a high enough level in the free version where you could unlock submarines in the premium version, the game will unlock them for you and let you view them in your drydock, but you'll only be able to play in them if you do the $10 transaction.
Currently, every possible thing I've seen that can have money spent on it would cost just under 16 USD altogether. This breaks down into the $10 to get the premium version, 99 cents for each of five stylized historical submarines, plus taxes on all of them. There's no way that I know of to spend money on anything else.