Kalaallisut (standardised West Greenlandic) and Inuktitut are essentially dialects of the same language: but with the former being spoken on (in?) Greenland and the latter in Canada, there are differences that are due not only to the separation but also to the contact with different Westerners: Danes in Greenland and Anglos in Canada.
The most obvious influence is loanwords: Kalaallisut tends to borrow from Danish, Inuktitut from English.
But another fun difference is in the meaning of the root qallunaa-: from my brief exposure to the languages, it seems to refer to the “default” foreigner, and so in Kalaallisut, qallunaatut “like a qallunaaq; like qallunaaqs” means “Danish language”, while in Inuktitut, qallunaatitut “like qallunaaqs” means “English language”.
(This is essentially the same word; the extra -ti- in the Inuktitut version is a plural morpheme which isn’t present in Kalaallisut because that language no longer has a separate plural form for the equative case.)
(As another note, the Inuktitut Wikipedia glosses qallunnaaq [sic, though the syllabics only have one -n-] as
Caucasian, anglophone, southern, non-Inuk.)