So far, the we have the following ship-types in Rome II:
Egypt:
Missile Penteres (five-rower with archers), Flagship Octeres (eight-rower with Infanterie), Artillery Penteres (five-rower with onager).
Romans:
Assault Quadreme (four-rower with infantry), Artillery Quinquereme (five-rower with ballista))
There are similar buttons as in Shogun 2 - the usual missile button and the ones for grouping, formation, speed, stop, close combat, fire arrows. There is also an "board ship"-button that makes your ship ram the the others. But I don't know what the button on the far right of the flagship means.