FRIGATES - these are long, relatively light vessels with a lot of guns - more than 28, if you want to get technical about it. Frigates were light and easily maneuvrable, so they were often used for reconnaisance, or escorting merchant vessels. "Frigate" is also a terrific word to use if you want to swear but your mother-in-law is nearby.
GUNBOATS - These were smaller vessels, generally containing only one gun - but it was a really big gun. The gun in the boat is where the term "gunboat" gets the word "gun" from - it's not known why the word "boat" is there. Gunboats were relatively inexpensible to build, and could be assembled quickly. They were most often used to bombard targets on land. Although gunboats can easily be destroyed by a larger ship - such as a frigate - several gunboats together could do some serious damage before a larger ship could destroy them all. Strength in numbers. And guns, of course. Mostly guns.
SCHOONER - Schooners are small, light craft, noted for their speed. These were the preferred ships for privateers during the American Revolution - there was nothing better for breaking through enemy lines faster than you could get shot at - or for making a fast getaway. Nowadays, of course, we have jet skis.
Man O' War - This isn't really a naval classification, but more of a catch-all term for a warship carrying a lot of cannon. Most of the Man o' Wars you'll see will likely be Ships of the Line, which are essentially big ships with multiple gun decks stacked on one another. Basically, naval warfare consisted of lining up your ships broadside against the enemy's ships in order to hit them with the most cannonballs possible. Of course, the enemy would be trying to do the same thing. Predictably, the biggest ships with the most guns usually won - leading to the building of more ships, with even bigger guns. It wasn't sophisticated, but by God, it worked.