The Commonwealth is essentially the former members of the British Empire, who share a common monarch (the Queen) but are otherwise totally separate countries. Canada was an independent country by the time of the 2nd World War, but remained a close ally of Britain and joined the war in support. Other countries, like India, were still part of the Empire in the 2nd world war, and indian soldiers were part of the British Army.

In the First World War, most of the Empire was still intact (although Canada was technically independent, but Britain still handled their foreign policy) and Australian, Irish, South African and New Zealand soldiers, as examples, were part of the British Army.

America left the Empire after the Revolutionary war, so never became part of the Commonwealth