Im thinking about purchasing the GM2, but there are so many different versions, desktop, web etc.
What do I get with desktop version? Is this a full version, and whats the difference between publishing to windows vs web?
The "versions" as you called them are really just export modules. The modules you own determine which target platforms you can export your game to, to put it simply.
Creator licenses and the Ultimate license are 12 month subscriptions. The other ones are permanent.
Everything that's not Creator (or Trial) is a "full version" - that is, any active license grants you access to all features. Creator grants you access to most features.
The Desktop license therefore is a permanent 2.x license that grants you access to all features and all Desktop exports (Windows, Mac OS, Ubuntu).
The difference between publishing to Windows vs Web is that a game published to Windows will run under supported Windows operating systems, while a game published to Web will be hosted on a website and run in a browser.