This question was recently posted on the Inuit-Yupik-Unangan Discord group, and user zanewallach gave this fantastic answer, which I’m sharing with you all below (the above map from Wikipedia by Noahedits may be helpful):
ehhh… it’s a complicated question to answer, but Inuit languages work on a spectrum. Pick a spot on the map, and the further west or east you go, the less you’ll understand. Generally, all the Inuit dialects in Nunavut, including North Baffin, South Baffin, Aivilik, Kivalliq, Nunavik, and Nunatsiavut, are mutually intelligible for native speakers without much effort. These dialects share the vast majority of their basic vocabulary (although some surprisingly basic things such as greetings and the words for ‘yes’ and 'no’ are different from dialect to dialect) and the main way that they vary is in terms of gemination (generally, the more west you go, the less gemination occurs). That being said, it makes sense to classify the aforementioned group of dialects under a single name: Eastern Canadian Inuktitut. So, there are basically four main dialect groups which, for the sake of simplicity, can kind of each be considered their own language. Another way to look at it, is that Inuit is one huge macrolanguage, but I think the former approach is more practical.
The four major dialect groups (or languages) are these: Inupiatun dialect group = North Slope, Malimiutun, Qawariaq, Bering Strait Western Canadian Inuktun dialect group = Siglitun, Inuinnaqtun, Natsilingmiutut Eastern Canadian Inuktitut dialect group = North Baffin, South Baffin, Kivalliq, Aivilik, Nunavik, Nunatsiavut Greenlandic dialect group = West Greenlandic, East Greenlandic, Polar Greenlandic
Keep in mind, most all these dialects have subdialects, but at that level, it’s most just quibbling If we start with North Baffin, Inuinnaqtun is where it starts to become a legitimately different language, but still, I think a native speaker from Iglulik would be able to understand 80% at the very least of what a native speaker from Ulukhaktok was saying. North Baffin compared to Greenlandic is where the differences start to become pretty insuperable, but I still think someone from Nuuk could understand 70ish% of what someone from Iglulik was saying if they were trying their hardest. (But probably less so, the other way around) Theoretically, the two furthest Inuit dialects apart from each other are Bering Strait Inupiaq and East Greenlandic. I don’t think that speakers of these two dialects would understand more than 20% of what each other were saying Here is a list of basic North Baffin Verb Roots next to their Inuinnaqtun equivalents for comparison:
isuma- = think / ihuma- pisuk- = walk / pihuk- titiraq- = write / titiraq- niri- = eat / niri- katak- = fall / katak- sinik- sleep / sinik- tikit- arrive / tikit- taku- see / taku- ikajuq- help / ikajuq- malik- follow / malik- tautuk- watch / tautuk- pilak(si)- = carve / pilak(hi)- kapi(si)- stab / kapi(hi)- ingit- (iksivaaq-) = sit (be seated) / ingit- (ikhiva-) aullaq- = depart / aullaq- angirrau- (angirraq-) = go home (be at home) / angilrau- (angilraq-) tusaq- (tusaa-) = hear / tuhaq- (tuhaa-) tuqu- (tuqunga-) = die (be dead) tuqu- (tuqunga-) iqqaq- (iqqauma-) = remember / itqaq(gi)- qauji- (qaujima-) = discover (know) / ilihima- tukisi- = understand / kangiqhi- qukiq(si)- shoot / hiqquq- naulik(si)- harpoon / naulik(hi)- kunik(si)- = kiss / kunik(hi)- ilira(suk/gi)- = intimidate / ilara(huk/gi)- quvia(suk/gi)- = be happy / quvia(huk/gi)- kangu(suk/gi)- = be shy / kan'ngu(huk/gi)- naglik(gusuk/gi)- = love / piqpa(gi)- piu(ksak/gi)- = like / nakuu(gi)- unga- = miss / kinnguq- As you can see, with basic vocabulary, the differences between East Canadian Inuktitut and Western Canadian Inuktun are very minimal. That’s why sometimes, both dialect groups are labeled under the name “Inuktut” But Greenlandic shares a lot less vocabulary with these dialects The good thing though is that all Inuit languages have essentially the same grammar as each other (they are all equally polysynthetic as one another), but some dialects are more vague about tense than others, North Baffin has one extra mood than the other dialects, aspect works a bit differently in Western Canadian Inuktun than it does in Eastern Canadian Inuktitut; stuff like that. It’s really in the phonology that dialects vary the most.