That's a great idea, figuring there are 13 American Commonwealths according to Fallout's lore. Fallout 4 takes place in one of them, so it seems odd to call it THE Commonwealth.
Fallout 4 is set post Nuclear Summer in presumably the first Autumn since the war. Thus why so many of the inhabitants are wearing jackets and why the Commonwealth isn't generally referred to as a wasteland. In fact, the Capital wasteland probably isn't a wasteland anymore by this period either.
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Also, New Vegas is not canon.