Each land claim has different ways in which they've created rules around land tenure. So in the Nunavut case, the Inuit-owned lands are owned by the collective. Individual Inuit do not own individual parcels of land in fee simple. Inuit development corporations or Inuit representational organizations hold those lands as a collective.
Other jurisdictions have other land regimes. The land regimes in Nunatsiavut go back to the 1700s with the Moravian Church. There is fee simple ownership in communities in Nunatsiavut in ways there that aren't in other Inuit regions.
Just broadly, in the land claims settlement regions, and the 14% to 17% of the settlement areas that are owned in fee simple by Inuit, those lands under comprehensive land claims agreements are owned in a collective, not in an individual sense. What happens in the municipalities often predates the settlement of the modern comprehensive land claims agreements.