Below is a table showing the relationship between these two methods, limited to fiber types found in humans. Note the sub-type capitalization used in fiber typing vs. MHC typing, and that some ATPase types actually contain multiple MHC types. Also, a subtype B or b is not expressed in humans by either method .  Early researchers believed humans to express a MHC IIb, which led to the ATPase classification of IIB. However, later research showed that the human MHC IIb was in fact IIx,  indicating that the IIB is better named IIX. IIb is expressed in other mammals, so is still accurately seen (along with IIB) in the literature. Non human fiber types include true IIb fibers, IIc, IId, etc.