Grammatically, there is no way to say whether the four directions are merely indicating which half of the street, road, or avenue you're on. This is not an English Language & Usage question but an empirical question that has to be asked at the city hall in the town with those street names.
If there are many other streets with state names (e.g., South Carolina Ave., Georgia Ave., New York Ave.), then there's a state theme. If not, who knows?
West America Street's probably the western section of America Street, but then there'd have to be an East America Street to confirm that.
One orthographic clue is if the directions are abbreviated as N., S., E., and W.: N. Carolina Ave. is probably the northern section of Carolina Ave. But it's still an empirical question that has to be answered at City Hall.