You seem to know a lot about ships and sailing. So I thought I might aks you some things.
Could you help me to relatively compare the ships below with other ships?
I just have a general interest in the golden age of sail. Mostly Britain and America. Other guys are borderline historians (Walter).
The names of these ships refer more to the rig than the ship itself.
A brig has two square sail masts rather than three like a "ship rig". The "naval" in name just means it is for military use by the navy, rather than being a private merchant ship.
A cutter has a single mast, and three or more stay sails ( the sails on forward mast stay ropes).
A schooner has two masts with fore and aft sails. Modern ones have a single triangular bermuda sail, but tradionally they would have had a gaff sail with separate top sail.
A barque is like a "normal" ship rig, but the mizzen mast has fore and aft sails like on a schooner.
Navies generally stuck to square rigs like the Brig and Ship Rig. Square sails are generally faster in favorable winds. But less maneuverable, and in contrary winds may have to wait for weeks for the weather to change. They also require large crews to climb the rigging to set the sails. Very expensive for a merchant ship, but not a problem if you can just impress the crew or have extremely valuable cargo.
Fore and aft sails(schooner) are more maneuverable, and can sail into the wind much more easily, and don't require as large a crew to sail. But, are more difficult to sail and not as fast in favorable winds like a square rig would be. They require an experienced crew to sail well. Not something you would trust to impressed crew that has never sailed before. A barque is a compromise between the two extremes, and has the qualities of both to a degree.
The cutter is small ship. Most were pilot boats to bring the harbor pilot to ships to guide them in. A Naval Cutter would be an armed version for interdicting smugglers close to harbor.
The brig is the economy/budget version of a frigate. They lack the firepower of a frigate, and also the cargo space to carry enough food and water for long range cruising. But, they require a smaller crew, and with the invention of the carronade they could have the firepower of a small frigate.
The schooners were mostly fishing boats or cargo ships. The British tried using these, but found they were too under powered and dangerous to sail to be of use. For the most part these were private owners that fitted them with guns for privateering.
Like a said earlier. The names refer more to the rig than the ship itself. A full rigged ship like a frigate could be decommissioned, and sold to a private owner. The guns removed and re-rigged as a barque. Then spend the rest of its days hauling manufactured goods to the americas, and rum/sugar back to Liverpool.
Larger than/ More Cargo space/ Stronger in Combat are all generally the same (I think).
Cutter < Schooner < Brig < Barque
"Faster than", and "Easier to Navigate" I'm not so sure about.