The game is free here and there is a free demo on Steam. But there is also a paid version on Steam. Are all the versions the same? Does the paid version have more content/features?

The demo on steam and itch.io are the same.
The full versions includes 3 single player campaigns, invasion game mode, map editor, modding support, access to the Steam Workshop, achievements. Online multiplayer also works directly through Steam without having to worry about port-forwarding.