This seems like a straightforward question, but it’s not. The simplest answer is that Inuktut is the Inuit language as it is spoken in Nunavut. The Government of Nunavut slected the term Inuktut to represent all of the Inuit dialects spoken in Nunavut, including Inuktitut and Inuinnaqtun. In this way Inuktut is recognized as a single language.
Inuktut is just one part of what is known as “the Inuit language”, spoken from Alaska in the west to Greenland in the east. It might best be understood as a spectrum of dialects that vary enormously from one end of the Arctic to the other. Communities close to one another generally have few problems communicating between dialects, whereas an Alaskan and a Labradorian would not be able to.
Even within Nunavut, vocabulary and pronunciation vary from place to place and between generations. Up until 50 years ago, most Nunavut Inuit lived in isolated camps where distinct speech forms evolved. As they settled into permanent communities, speakers of varying dialects often became neighbours in the same hamlet. This mixing has intensified with the modern-day migration of Inuit in search of employment and opportunities in other communities.
Daily life helps break down communication barriers. So, too, does media, like CBC (Canada’s national radio and television broadcaster), by exposing Inuktut speakers to a range of dialects spoken throughout the territory. Today, fluent speakers in all parts of Nunavut can normally understand each other with only minor difficulties.