Main Difference
The main difference between Mammoth and Mastodon is that the Mammoth is a extinct genus of mammals and Mastodon is a genus of mammals (fossil)
Mammoth
A mammoth is any species of the extinct elephantid genus Mammuthus, one of the many genera that make up the order of trunked mammals called proboscideans. The various species of mammoth were commonly equipped with long, curved tusks and, in northern species, a covering of long hair. They lived from the Pliocene epoch (from around 5 million years ago) into the Holocene at about 4,000 years ago, and various species existed in Africa, Europe, Asia, and North America. They were members of the family Elephantidae, which also contains the two genera of modern elephants and their ancestors.
The oldest representative of Mammuthus, the South African mammoth (M. subplanifrons), appeared around 5 million years ago during the early Pliocene in what is now southern and eastern Africa. Descendant species of these mammoths moved north and continued to propagate into numerous subsequent species, eventually covering most of Eurasia before extending into the Americas at least 600,000 years ago. The last species to emerge, the woolly mammoth (M. primigenius), developed about 400,000 years ago in East Asia, with some surviving on Russia’s Wrangel Island in the Arctic Ocean until as recently as roughly 3,700 to 4,000 years ago, still extant during the construction of the Great Pyramid of ancient Egypt.
Mastodon
A mastodon (Greek: μαστός “breast” and ὀδούς, “tooth”) is any proboscidean belonging to the extinct genus Mammut (family Mammutidae) that inhabited North and Central America during the late Miocene or late Pliocene up to their extinction at the end of the Pleistocene 10,000 to 11,000 years ago. Mastodons lived in herds and were predominantly forest-dwelling animals that lived on a mixed diet obtained by browsing and grazing, somewhat similar to their distant relatives, modern elephants, but probably with greater emphasis on browsing.
M. americanum, the American mastodon, and M. pacificus, the Pacific mastodon, are the youngest and best-known species of the genus. Mastodons disappeared from North America as part of a mass extinction of most of the Pleistocene megafauna, widely believed to have been caused by overexploitation by Clovis hunters.
Mammoth (noun)
Any species of the extinct genus Mammuthus, of large, usually hairy, elephant-like mammals with long curved tusks and an inclined back, which became extinct with the last retreat of ice age glaciers during the late Pleistocene period, and are known from fossils, frozen carcasses, and Paleolithic cave paintings found in North America and Eurasia.
Mammoth (noun)
A mastodon.
Mammoth (noun)
Something very large of its kind.
Mammoth (adjective)
Comparable to a mammoth in its size; very large, huge, gigantic.
Mastodon (noun)
Extinct elephant-like mammal of the genus Mammut that flourished worldwide from Miocene through Pleistocene times; differs from elephants and mammoths in the form of the molar teeth.