Latte is very milky. It's hot milk, with a shot of espresso added. As opposed to black coffee, with a dash of milk (or cream).
Cappucino is latte only frothier. I think. I've never been sure of the difference. I do know that a cappucino is named after a type of monk (the Capuchins) who wore a brown robe with a white hood...
I think what you're having is an Americano (expresso shot plus hot water) with cream.
Mocha is coffee and chocolate, and oddly, I've never ordered one. I should.