"Chai" literally means "tea" in Hindi, with cognates in other North Indian languages. The British introduced tea to India, and the spicy, milky drink so often called "chai" is "chai masala" in Hindi, "masala" referring to the mix of spices the Indians put into the industrial quality reject tea they were encouraged to drink in a campaign to drive up local consumption. So it would be nearer the mark to describe the sort of drinks sold as "chai" as "masala", since it's the idea of a mix of spices they have in common, not necessarily having any connection with tea, as in the extract of the Camellia Sinensis leaves.

Interestingly (to language nerds anyway) the the words "chai" and "tea" both come from the same Chinese character for the Camellia Sinensis. One spread to South Asian languages via Cantonese, the other spread to various European languages via Mandarin.