Well,
In the age of sail, anything with fewer than three masts was not a ship. On the other hand, two-masted vessels like brigs and brigantines would also have boats stowed on them.
Conversely, there were some fore and aft rigged ...um... nautical floaty things that had three masts, like French xebechs (or chebecs) that were not "ship rigged" with square sails. I'm not sure if they were considered "ships" or not.
Regards,