Strictly spoken, rigid is not a washing type at all because this term is used by Levi's for jeans which are not washed, but are made from raw, unwashed denim.
Contrary to the general meaning of "rigid", the term does not mean that the material is very stiff. The material used by levi's for their rigid jeans widely varies. It may for example be heavy-weight denim or light-weight denim.
Even if Levi's shrink-to-fit jeans are often offered in rigid, the terms should not be confused with each other, either. Rigid jeans are available both made from pre-shrunk denim and from unshrunk denim.