Members of the
Commonwealth of Nations do not exchange
ambassadors with each other or have an
embassy in another member: they have High Commissions instead of embassies, and exchange High Commissioners. No doubt this is a relic of the gradual process of
independence the early members went through, back when they were
dominions in the
British Empire. With the
Statute of Westminster in 1930 it was made explicit that member states were all fully independent equals.
Idi Amin caused a bit of a diplomatic tiff by insisting that his representative in London was an ambassador, not a high commissioner. Of course, our Idi did like the titles and made himself Field Marshal, V.C., and King of Scotland. Subsequently Ugandan governments have been content with the tradition of high commissions.
The term is sometimes used in other contexts. There is a United Nations High Commissioner for Refugees. Britain's three East African colonies of Kenya, Uganda, and Tanganyika were administered together by an East African High Commission between 1948 and the time they started peeling off for independence in 1961.