Actually, in period parlance, the 'Corsair' is indeed a Brigantine, and includes square sails and fore-and aft gaff sails on BOTH masts. In modern parlance, the Brigantine ordinarily does not have square sails on the main mast, but there is ONE existing true brigantine with the proper rig, and it is named 'Eye of the Wind.' Have look at the following reference: http://sailing-ships.oktett.net/brigantine.html and here: http://en.wikipedia.org/wiki/Hermaphrodite_brig
'Prince de Neufchatel,' which has the same rig as the Aurora 'Corsair' is variously referred to as either a schooner or a brigantine, depending on whether the author is using old, or modern parlance. To make things even more confusing, sometimes this rig is referred to as a 'schooner-brig,' or even 'hermaphrodite-schooner.' All are correct, but 'topsail schooner' is not!
As for Baltimore clippers, they are characterized by 'sharp' hulls (in cross-section, and in plan), with heavily-raked masts, ordinarily a lot of drag aft in the keel, and an enormous sail-plan for their size.