mammoth — any large, elephantlike mammal of the extinct genus Mammuthus, from the Pleistocene Epoch, having hairy skin and ridged molar teeth.
mastodon — a massive, elephantlike mammal of the genus Mammut (Mastodon), that flourished worldwide from the Miocene through the Pleistocene epochs and, in North America, into recent times, having long, curved upper tusks and, in the male, short lower tusks.
pachyderm — any of the thick-skinned, nonruminant ungulates, as the elephant, hippopotamus, and rhinoceros.
tusker — an animal with tusks, as an elephant or a wild boar.