That's rather incomplete.
British classified warships during 17-19th century solely based on number of guns. 28+ were frigates and 50+ were ships of the line, while those with less were called sloop-of-war, which could be then classified based on design. so there were Bermuda sloops, brig-sloops, snow-sloops, ship-sloops...
French based it on design and purpose as well as armament. Corvettes were always three masted ships, but smaller than what French considered a proper frigate. Most of the time they were full ship-rigged, but larger Bermuda sloops were considered corvettes too. Smaller vessels were classified based on design, so they were simply designated as brigs, snows, cutters...
The issue though is that we're talking about development of late 17th and 18th centuries when galleon design was gradually replaced by frigate and full-rigged ship design. A major part of game takes place before that. Which is why I felt it's better to have race-built galleon as primary anti-pirate vessel, as the design was used from 16th until mid-18th century for cruiser operations.