The lowers are the jib, stays''l, fores''l, and mains''l. If a schooner has uppers (mine does), you can hoist a fisherman stays''l (between the masts), and if it is gaff-rigged (mine is), you can hoist a jackyard tops''l (triangular sail that fits in the slot above the main).
To add to Schooner man''s answer, if you have a ''coaster'' style schooner with almost equal gaff main and foresails you can also hoist a foresail top which is a triangular sail that fills the triangle between the foresail gaff and the mast head. If you don''t have floating spars on your main topsail its is simply a main topsail. If you have a big four sided sail between the main mast and the foremast, it is a gollywogger. If you have a square sail on your fore mast you have a square topsail schooner and I believe the sail is a fore topsail (not to be mistaken for a Foresail topsail).
On a schooner, the forward most mast is shorter than the aftermost mast. The tallest mast is always the main mast. The forward mast is called the foremast, and the other mast, the aftermost mast, is called the main mast. If you are square rigged, the lowest, largest sail is called a course. In order to tell someone what sail to do what with, you have to locate the sail. Sails are named according to the mast they are on. The forward course, the one on the foremast is the forecourse. The aftermost course is on the main mast; thus, it is the main course.
Above those, you have the fore topsail, and the main topsail. On a square rigger, you would then have the upper fore topsail and the upper main topsail. Following that, you have the fore sky sail and main sky sail. And, then, you would have the fore and main moon sails. If you are in very light air or heavily laden, there are temporary, portable sails that are hung on their own small yards off the fore and main yards to give you extra
sail area. These are called dunnage sails. Most schooners are fore and aft rigged. Thus you have the foresail and the main sail. Sails forward of the foresail are refered to as jibs normally. Jeff has well described the
triangular sails above gaffed fore and main sails. They are topsails. Again, they are named after the mast they are on. That is, the fore topsail, and the main topsail. In a puff, the vessel can be depowered by simply allowing these topsails to drop behind their respective, lower, larger sails rather than securing them. This is called "scandalizing".
P.S. On very large square riggers, there will
be even another sail in the mix. Then, you will have, from top to bottom, the fore course, the upper fore sail, then the fore top sail followed by the sky and moon sails.
I mention this because I know good and well Jeff was going to call me on it. dhd