Monday Mammmal #11: Mastodon or Mammoth?

So which one's which, and what's the difference?  Who lived where, and when did they live there?

You can learn more about mastodons and mammoths from the The Field Museum in Chicago, jump ahead to their page on how to tell the difference between the two (or here from the Smithsonian), read more about Mastodons here, more about Mammoths here and more about the group as a whole here and here.