Masala means "blend of spices" "Garam masala" is a blend of hot spices, "chai masala" is meant for making tea, In the US, Chai usually refers to Indian style tea with milk and spices. Source: I've worked with a lot of Indian people.
As an Indian I want to put this on record, the spiced tea is absolutely obnoxious. We do not drink it. There is a different one flavored with ginger or cardamon, which people like and tastes so much better than 'masala chai' sold in US etc.
Indian here too. We do drink masala chai in India (Gujarat).
We have a few who do garam chai with their chai pani, too.
The call center beverages seen in "Slumdog Millionaire" appeared to me to be some sort of hot milk+tea beverage. At the time based on sources I had already read, I thought this would be spiced. I remember that in the movie, each serving was in a decent size drinking glass of about 10-12 oz and the glass was wrapped with what appeared to be a paper napkin. For some reason this is stuck in my mind.