Is Rainbow Loom different than Cra-Z-Loom?

Kind of. Rainbow Loom is the first rubber band loom. Cra-Z-Loom is the same thing, just by Shimmer'n'Sparkle.

The Cra-Z-Loom is an imitation of the official Rainbow Loom. However, imitation brands may not be as high quality as the official Rainbow Loom.