From what we have gathered so far, from posts and the KS, and the options listed on the Alpha it seems we will have the following options.
Multi Player Online: - Free for all PvP universe we see and take part in the evolving environment. Lots of players interacting.
Single Player Online: - You play in the live universe, server based, but do not see other players but you do see the changes that are made by other players, within reason.
Multi Player Co - Op: - Similar to MPO but you only have a selected group of people you see and play with.
Single Player Offline: - You play on your own PC only. Only changes you see are the ones you make. You can update your universe with data from the server if you log on and update.
Also remember that you cannot switch back and forth. If you make a character on a single player offline version you cannot move it to the Multiplayer once it gets well equipped etc.
Note: These are subject to change as are all things.