A schooner is a vessel of two or more masts, generally all fore and aft rigged. Actually, the term covers a variety of types, with the first forms emerging in the Chesapeake Bay area of America in the 18th century. They were used for coastal trade, fishing and even as small naval and customs vessels.
Dating from the early 1800s, the Baltimore schooner is the first named type and is acknowledged internationally as having revolutionised shipbuilding. The hull was designed with a sharply sloping bow and stern, drastically increasing deck length compared to the waterline. The keel deepened towards the stern, improving the balance of the craft. These and other improvements made this vessel, and other schooners, a popular design for a fast, economical carrier of freight and passengers in coastal as well as open waters. It was a topsail schooner, in that above the fore and aft rigged sails were square-rigged sails, either on both masts, or on the foremast only. These became obsolete in the middle of the 19th century and were replaced with triangular topsails using the,gaff as their boom.
Gaff-rigged schooners have come in versions with from 2 to 6 masts, with or without square-rigged topsails. (The longest wooden-hulled ship ever built was the 6 masted gaff-rigged schooner "Wyoming", built in Bath, Maine, in 1907. Even larger was the iron-hulled schooner, "Thomas W. Lawson", built in the 1890s in Quincy, Mass. It was 5000 gross tons weight, 385 ft long, and its seven masts were each 193 ft high. She was able to be sailed with a crew of only 16!)
Schooner rigged yachts were originally two or even three masted pleasure craft, gaff-rigged until the advent of Bermudian rig in the early 1900s, which negates the need for topsails and offers a corresponding lessening of the workload when cruising or racing. (It was the two masted schooner-yacht, “America” which won the original America's Cup in 1861, and after which the contest is named.)
The hermaphrodite-brig is also known as a “schooner-brig” or “brig-schooner”.
A "Gloucester schooner" was a specially designed North American schooner of the 19th century used for cod fishing off Newfoundland. Its hull looked somewhat along the lines of a schooner yacht's, but more sturdily built and it was gaff-rigged on 2 or 3 masts with up to 3 jibs forward of the foremast, and provision for topsails if required. It carried many "dories" (small 2-man rowboats) stacked on deck for the fishing. It was capable of getting the catch back to port at speed in various weather conditions.
Terms in 'bold can be found in Sailing ship types: Glossary
Reference: "The Oxford Companion to Ships and the Sea."