Purists like me would object to Chai being referred to its redundant form Chai Tea :)
Everyone knows what chai tea is referring to. In the same way they understand what naan bread is.
In India, chai specifically means tea with milk. It’s not just any “tea”. It’s fine to use, but not entirely accurate.
So the usage is all over the place.
Citation needed with the part of India referred to here.
> Masala chai is a popular beverage throughout South Asia, originating in the early modern Indian subcontinent. Chai is made by brewing black tea (usually CTC tea) in milk and water and then sweetening with sugar. Adding aromatic herbs and spices creates masala chai, although chai is often prepared unspiced.[2][3]
Still, rude to correct someone for using what's essentially a colloquialism. If enough people use a word 'wrong' then, well, that's a new usage that we can't ignore or get prescriptive about. Because prescriptive usage is from some point of view after all. The Chai tea people have their point of view, and are correct within their community.
I suspect that if we venture into the streets of an American city and interview random passers-by, fewer than 10% will know that "chai" is a word that already means "tea".
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.
[1] https://qz.com/1176962/map-how-the-word-tea-spread-over-land...
Masala Chai = Chai + spices (masala)