Indians can refer to spiced tea as "masala chai", but I almost always just heard "chai" - I guess that's the way it's so often prepared that the spices are implied?
Definitely no refilling with hot water! As the whole process takes time, I used to make 3-4 cups in the morning and take the remaining tea in a thermos to work.
A "Masala Chai" is milk, water, green tea leaves, tea, cardomom, cloves, grated ginger, a leaf of tulsi and a bunch of other stuff according to taste.