Rainbow moonstone is a feldspar mineral, a transparent labradorite with a pearly, opalescent Schiller (a variety of iriscent colours). Although not actually moonstone, it's similar enough that it is accepted by the gemstone trade as a gem in its own right.
Moonstone is an opalescent variety of orthoclase that evokes moonlight. The cause is the reflection of light by the internal structure, made of strips of albite and orthoclase. If the layers are sufficiently small, they give a nice blue, otherwise adularescence, white, is less popular.