Next year (February/March) they'll release so called FPS module, which is basically stripped down version of your average online shooter. Standard game modes, lobby based multiplayer, probably 6 vs 6 or 8 vs 8, squad based close combat fighting on small/medium sized maps. Bunch of different weapons, grenades and gadgets. Expect basic stuff like scoreboard, but don't expect achievements and weapon upgrades like in CoD/BF.
'Shortly' after that, they'll release something called social planetside module which should be ingame lobby filled with avatars where you'll probably be able to run around hangar, visit some bar and other places and go to dogfighting/racing/fps arenas. At that time multicrew ships should be playable (some of them). That will be the cornerstone of persistent universe design, something that will be upgraded with vast space, other planets, star systems etc. Loading screens will be minimized/concealed/eradicated over time.
FPS in finished game will be present in form of 'simulation' which is aforementioned lobby based arena fighting, boarding on ships, outside ships (on top of hull), in mining facilities, asteroids and specially designed planets which will be lawless and open for 24/7 fighting like in Planetside 2. They will also create lawless pockets on every planet over time, after release so you'll be able to leave cities and go into wilderness. But not at release. Only dedicated planets for that sort of stuff.