How is chai tea used differently in America then? If I ask for it in a coffee shop, I usually get chai (tea) with steamed milk, which is exactly what the original usage is.
Looking at the Starbucks app right now for example on their menu: Chai tea is black tea with clove, cardamom, cinamon, and ginger and no milk by default, Chai Tea Latte is that black tea and spices with steamed milk. You'll also see Chai sometimes to refer to the spice mix sold without any tea.
In my local coffee shop, I get black tea with steamed milk (called chai tea).
They also sell masala chai, which is the above + spices added.
Starbucks uses chai tea and chai tea latte to mean something else.
Some grocery stores (Trader Joe's?) sell chai as just a spice mix.
So Americans aren't really using it "differently" as much as they're using it wildly inconsistently. That's not really the same as cappuccino vs latte, is it? Latte is at least used to mean the same thing across the country.