An interesting question. Essentially, the Commonwealth countries are those which are former colonies of the British Empire - even though at various points in recent history some of them were technically NOT members of the political organization called the Commonwealth. For example, South Africa was suspended from the Commonwealth during the apartheid era, but South African writing in English from that era might still be known as, or described as, Commonwealth literature.
What is equally interesting is the way the terms have changed. One hundred years ago, scholars referred to such writing as 'Empire Writing'; then it became knoiwn as Commonwealth Literature; now Post-Colonial Literature is the favoured term.
Of course, all that I have written above excludes American Literature, since the USA achieved its independence at such an early point in history and has always been seen as wholly distinct - even though it was once a British colony.