Please note that while MWLL version 0.3 is exclusive to Crysis, MWLL version 0.4 (expected: "soon") will support both "Crysis" and "Crysis Wars". In the future, from either community preference or dev decision, it is possible Crysis Wars will end up the de facto if not actual only supported platform.
Crysis Wars is the standalone multiplayer component that comes with Crysis Warhead. (Though note that if you are getting Crysis Warhead digitally from EA store, be aware that apparently
you may have to download it separately.)
Crysis Maximum Edition contains both Crysis, and Crysis Warhead (which includes Crysis Wars).