Lime and gypsum are both related to calcium. Lime is considered to be one of three things related to calcium, which are carbonate, oxide, and hydroxide. Gypsum is considered to be only one thing in relation to calcium, which is a sulphate. Another difference between the two is related to their properties of alkaline.
Lime has a property that is more alkaline, whereas gypsum has more of an acidic property. Along with what they are comprised of, another difference between them is the type of crystals they have. Lime has finer crystals, whereas gypsum has crystals that are larger in size.