In languages all over the world, chai is the literal translation for the English word tea. In China, where tea originated, its cha. Masala chai, or spiced tea is probably the closest thing to a chai tea latte, but even thats stretching it.
Just “chai” is fine.
In China, where tea originated, it’s cha. Elsewhere, you have the “Russian chai, Persian cha, Greek tsai, Arabic shay, and Turkish çay.”
In South Asia, where corporations likely got the word, “chai” can be used to describe tea that’s been made black or with milk, with spice or without… IT’S ALL CHAI, BROTHER. “Masala chai,” or “spiced tea” is probably the closest thing to a chai tea latte, but even that’s stretching it. PSA: Chai Tea Latte Doesn’t Mean What You Think It Means