No, I think you have it right. I have lived in NYC and now live in SF, and a sensible comparison would be Manhattan to San Francisco, or the 5 Boroughs, northern Jersey and a chuck of CT to roughly San Jose up to SF. We can argue about including Marin.

(I generally look at urban regions that are larger entities than official borders by transit. If there are large daily people flows from area A to B, A and B are part of that region, no matter what the tax borders say.)