Cartilaginous fish, scientifically classified under the class Chondrichthyes, include all fish whose skeletons are made of cartilage rather than bone. This group includes sharks, rays and, less commonly known, chimaeras, which belong to the subclass Holocephali. The elasmobranchs are a subgroup of these cartilaginous fish and include only sharks and rays, excluding chimaeras.

Simply put, all elasmobranchs are cartilaginous fish, but not all cartilaginous fish are elasmobranchs.