Selenite is the clear, crystalline form of gypsum (a hydrous calcium sulfate). It is soft enough to scratch with a fingernail, shows one perfect cleavage into flexible (non-elastic) flakes, and does not react with acid, separating it from calcite.
In the evaporite sequence
Gypsum precipitates out of an evaporating brine before halite does, so a playa section often reads bottom-to-top as carbonate, then gypsum, then rock salt — find selenite blades and the halite crusts are usually nearby. Desert roses are the same mineral grown around sand grains in damp basin soils.