The Commonwealth of England has nothing to do with colonies. It was the English republic under Cromwell. NATO is a defensive alliance. CIS is a kinda-sorta successor to the Soviet Union in a way vaguely comparable to how the British Commonwealth is the successor to the British Empire.
But the latter is really the only commonwealth that actually has anything to do with colonies. Former colonies, though. There isn't really a proper meaning to the term commonwealth (aside of being the literal English translation of republic), so saying things like NATO is the commonwealth of the USA is meaningless.