The word morph itself, in Webster:
Morph:
2 a : a local population of a species that consists of interbreeding organisms and is distinguishable from other populations by
morphology or behavior though capable of interbreeding with them
b : a phenotypic variant of a species
Morphology:
1 a : a branch of biology that deals with the form and structure of animals and plants
b : the form and structure of an organism or any of its parts
Different forms (shapes/sizes/colors/patterns/etc) = different morphs.
In the general sense a mutation is a change. In the more specific genetic sense a mutation is a changed gene, and I think that is what is generally meant by "mutation." Some morphs are based on a specific genetic mutation or combination of mutations. IMO they can also be aptly called "mutants."
But other morphs are also based on selective breeding, which would be the accumulation of groups of genes, and there can be different genes causing similar looks in specimens of the same morph. So same morph does not necessarily mean the same underlying mutations.
Rich often uses the alternative "cultivar," which I think came from plants and is abbreviated from "cultivated variation." IMO it's interchangeable with morph.