Alabaster is a name applied to varieties of two distinct minerals. Gypsum is a hydrous sulfate of calcium, and calcite is a carbonate of calcium. Gypsum is the alabaster of the present day; calcite is generally the alabaster of the ancients. Both are easy to work. They are attractive to look at. Both have been used for making a variety of artworks and objects, especially small carvings.
The two kinds are easy to tell apart. One is harder than the other. Calcite is hard (Mohs hardness 3). Gypsum is soft (Mohs hardness 1.5 to 2). It can be easily scratched by a fingernail. Also, calcite effervesces when it is treated with hydrochloric acid. Gypsum does not.