Inuit is the term used by and for the Indigenous peoples of northern Canada and Greenland, and it is what you should use. Eskimo is widely considered offensive in Canada and Greenland and should be avoided. Usage in Alaska differs: Eskimo has been used there as a collective term because it covers both Iñupiat and Yupik peoples, who are distinct — but Alaska Native, or the specific people's name, is preferred.
The core difference
This is a question about which word to use, and it has a clear answer for most contexts.
- Inuit — the peoples of northern Canada and Greenland. The correct term there. Note that Inuit is already plural; the singular is Inuk.
- Eskimo — avoid. Considered offensive in Canada and Greenland.
- Alaska Native — the preferred collective term in Alaska, covering Iñupiat, Yupik and others.
Why Alaskan usage is different
Because Yupik peoples are not Inuit. Using Inuit as a blanket term across Alaska would wrongly absorb distinct peoples into a group they do not belong to, which is why a collective term was retained there longer. The modern preference is to name the specific people — Iñupiat, Yupik, Aleut — or to say Alaska Native.
Practical guidance
Name the specific people where you can. Where a collective term is needed: Inuit in Canada and Greenland, Alaska Native in Alaska. Eskimo survives in some older institutional names and historical quotation, which is the only context where you are likely to need to reproduce it.