His title is "His Majesty Charles the Third, by the Grace of God, of the United Kingdom of Great Britain and Northern Ireland and of His other Realms and Territories King, Head of the Commonwealth, Defender of the Faith" but he can claim many others. In Canada he is announced as King of Canada.
Yes, and he is also:
"Charles the Third, by the Grace of God King of Canada and His other Realms and Territories, Head of the Commonwealth"
https://en.wikipedia.org/wiki/List_of_titles_and_honours_of_...