Precisely. And the French call it the rez-de-chaussez, as I recall, though I never looked up the literal meaning.
A rare US building will have both, but usually there are extenuating circumstances, such as the building being built on a hill so both floors are on the ground...

But in general, in the US, when you walk off the street and onto an elevator you have gotten in at the first floor, which is also the ground floor, and may have either a "G" or a "1" on the button. (As well as the mandated star to tell you that's where the exit to street is.)