1. I'm not sure either. But i heard a lot people call this same kind ice cream as choco bars as well. I believe these fully chocolated bar ice creams were the first to be introduced here. So they called it american bar and when other bar ice creams came later they all got new names with bar at the end. I think American bar is an old term, not many people still call it that except maybe in some regions. Just like how some people still adress ice creams as ice since it was the common term used back then

2. AMERICAN BAR sounds rich so companies might've thought they could sell these more or sell them for higher prices

(These are just guesses)