Eskimos speak a number of languages. One problem is classifying them: Inuit seems to be a cover term, with Inuktitut being a fairly common term in Canada and being a distinct language variety. Yup'ik in the US is related, but Inupiatun (etc.) is more closely related. Think of it as a continuum of dialects with gaps--you start at one end and start walking, and the changes build up only gradually until they're pretty much mutually unintelligible, and you get to decide where the language boundary is. It's either arbitrary or social (sort of like the Czech/Slovak boundary, but even fuzzier).
I've heard that many American Eskimos reject being called Inuktitut or even Inuit, but Inuit is nonetheless the standard term in Canada and a lot of Americans have decided that's what American Yup'ik want to be called--and extend it to the Aleuts, for which it can't properly be used. "Eskimo" in Canada, as far as I can tell, is rejected as both obsolete and offensive.
Peary's Eskimos were Inuit, probably Inuktitut (but that's a guess on my part based on where he was).
A map is useful. I'll link to the American map; there's probably one or more Canadian maps at ethnologue.com as well.
http://www.ethnologue.com/show_map.asp?name=US&seq=20