You might want to revisit who’s incorrect.
Edit: Like in Italian Latte just means milk, but in English it means an espresso with steamed and then frothed milk on top, what would be called a cappuccino in Italy usually. Americans calling it a latte aren't wrong, they're just using a loanword to mean something different then the original language.
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.