British empire has 2 different meanings across 2 categories:
a former empire consisting of Great Britain and all the territories under its control; reached its greatest extent at the end of World War I; it included the British Isles, British West Indies, Canada, British Guiana; British West Africa, British East Africa, India, Australia, New Zealand
"the sun never sets on the British Empire"
The United Kingdom and its dependencies. It became the Commonwealth of Nations following the independence of most of its dependencies.