A schooner was, in the words of the Tenth Doctor, a "nice little merchant ship". He and Martha Jones materialised on board one in the Caribbean Sea in 1800 — the final year of the Quasi-War.
Judging by this example, schooners were exclusively wind-powered vessels, which had jibsails both fore and aft. The particular schooner on which the Doctor had landed had some number of cannons as well. (COMIC: Second Wave)
The Mermaid and Governor Ready were schooners. (PROSE: Of the Mermaid and Jupiter)