Although there is some disagreement as to whether Cypraea mus donmoorei is a
valid taxon, the shell which generally goes by that name is a large, deep
water variation/form/subspecies of Cypraea mus.  The nominate form (Cypraea
mus mus) lives in shallow (often wading depth) water, while C. m. donmoorei
is dredged offshore in moderately deep water.  C. m. donmoorei is usually
considerably larger then C. mus mus, and for its size it is considerable
lower, wider and heavier than C. mus mus.  As already noted by others, it is
also typically lighter in color, with wavy markings on its sides, though
color is not a very good criterion for distinguishing taxa.  The presence or
absence of lumps, bumps, or "horns" in these deep water shells seems to show
a complete range from totally smooth shells to grotesquely bumpy ones.  C. m.
bicornis is the deep water form with large tubercles on the shell.  C. mus
donmoorei is essentially the same as C. mus bicornis, but without the bumps.
The small, dark, shallow water forms (C. mus mus) don't develop these
tubercles as far as I know.
Paul M.