The term "sloop" for a specific class of naval vessel actually doesn't have much to do with the sloop rig; in fact, all the sloops I can think of were ship-rigged. The term goes back at least into the 1700s... I'll do a little digging and see if I can come up with something.
On May 21, 1861, Constellation took the Charleston-registered slaver Triton. As Confederate forces had opened fired on Fort Sumter the month before, Triton became one of the Union Navy's first captures of the war. Recalled with the rest of the squadron for Civil War duty, Constellation arrived at Portsmouth, NH in late 1861. Refitted, the ship was dispatched to the Mediterranean Sea to protect American commerce. This assignment was largely the result of Constellation's lack of a steam engine and deep draft which made it unsuited for blockading the Southern coast.