I'm a chemist, but I must have been sick that day.
Wiki to the rescue:
Lime can refer to calcium oxides, hydroxides and/or carbonates, while the mineral
gypsum is composed of calcium sulfate. So they're different compounds.
Both are ingredients of building materials. Calcium carbonate is a major component of cement, gypsum a minor one. Although there's such a thing as lime plaster, "plaster" commonly refers to plaster of Paris, which is made from gypsum.