When you think of America, do you think of 50 independent countries joined together, or one large country with 50 territories?
It's not a union, it's a nation. To me, the "united" carries more weight than the "states".
I'm closer to the first one in my view
Every state is sovereign subject only to the US Constitution. That means they have far more authority than a simple territory.
E pluribus unum. Whether the "pluribus" refers to people/origins/backgrounds (my usual interpretation) or states.
That is, I live in Colorado at present. I've lived in Ohio, Illinois, California, Oregon, that non-state DC, Michigan, and West Virginia, as well. In none of those did I feel I was living in a place fundamentally different than the others.
Well, except maybe in DC.