A longbow is a kind of bow.
A crossbow is a kind of bow.
Note that the exact wording is "Boats (S) of an army including men with bows" so the men do not have to be embarked, just somewhere in the army.
IMO if the army contains psiloi with any kind of bow, or bow-armed cavalry, or cataphracts for that matter, then all its boats (S) can shoot.
I'd draw the line at baggage depicting camp followers with bows though.