Rebate is a British term that means the same thing as the American term "rabbet" not to be confused with "rabbit", a cute fuzzy animal. The origin comes from French word "rabbat" which more closely resembles the American English spelling, see this Wikipedia article. The difference between a rabbet and a mortise is that a rabbet is cut along an outer edge of a board or other piece of wood while a mortise is a recess cut within the piece of wood. Examples of a mortise are a slot in a piece of wood that accepts a tenon such as rail and stile joinery; a round hole in chair legs that mates with the tenon on a stretcher spindle; and a round recess used for holding a piece of wood for turning. An example of a rabbet would be a step along the edge of a board for cabinet joinery. You could also use a rabbet joint in woodturning ... a two part hollowform for example. You've probably seen rabbet planes that are used to create a step along the edge of boards. On this side of the Atlantic, a rebate is money back on a purchase. That's also the most common usage on the other side of the pond.