Sloop
To most of us, a sloop is basically a sail boat, having a single mast that is fore-and-aft rigged. If there are two masts, it’s called a cutter instead (and is typically larger). There are other minor variations on this, each with a different name, but they are not ships of war and therefore might only figure in our work if our characters need a small, wind-powered vessel. Another option would be the galley (oar-powered long ship).
Sloop-of-war (Corvette)
This ship is not to be confused with a sloop. As its name implies, it’s a warship, having a single gun deck with eighteen guns. It is considerably larger than a sloop and often has two masts. Eventually, three-masted versions were built and then resembled a small frigate. However, a frigate is square rigged; sloops-of-war have varying sail configurations, from all square-rigged to ketch riggings or snow riggings (googling this will reveal familiar images). The name corvette was later applied to them. The ships are not rated, having too few guns for the rating system of Britain, but we can rate them as we like on our world (i.e., seventh rate).