Which of these were the semi-independent polities under the British Crown?
The Dominions were the semi-independent polities under the British Crown that constituted the British Empire, beginning with Canadian Confederation in 1867. "Dominion status" was a constitutional term of art used to signify an independent Commonwealth realm; they included Canada, Australia, New Zealand, Newfoundland, South Africa, and the Irish Free State, and then from the late 1940s also India, Pakistan, and Ceylon (now Sri Lanka). The Balfour Declaration of 1926 recognised the Dominions as "autonomous Communities within the British Empire."
Earlier usage of dominion to refer to a particular territory dates to the 16th century and was used to describe Wales from 1535 to 1801 and New England between 1686 and 1689.
A distinction must be made between a British "dominion" and British "Dominions". The use of a capital "D" when referring to the 'British Dominions' was required by the United Kingdom government in order to avoid confusion with the wider term "His Majesty's dominions" which referred to the British Empire as a whole.
All territories forming part of the British Empire were British dominions but only some were British Dominions. At the time of the adoption of the Statute of Westminster, there were six British Dominions: Canada, Australia, New Zealand, South Africa, Newfoundland, and the Irish Free State. At the same time there were many other jurisdictions that were British dominions, like Cyprus.