It's all coffee. Basically the difference between espresso and drip coffee is the extraction method. Espresso is finely ground coffee put in a special basket and pushed through this basket with a lot of force for a short period of time; whereas drip coffee is ground coarser and usually extracted through a gravity drip method.
As for the difference in the types of drinks you inquired about: espresso, latte, and mocha. Espresso is just a straight shot of coffee made from the espresso machine without any thing else added to it. The latte is milk steamed to a velvety consistancy and blended with the espresso shot, and the mocha is basically a latte with chocolate added.
a little more detail should go into this drink identification, as there's some very good and popular drinks undefined here. Let's see we've established coffee, espresso, latte, and mocha, let's get on with the list
Cappuccino = 1 shot espresso and equal parts steamed milk and foam
Macchiato = a shot or two of Espresso and a dollup of foam...Star$$$ makes a drink by the same name, but it's something different and I dont remember what
Cafe au Lait = kinda like a latte but without the foam. I never tried, but what's the difference?
Depth Charge/shot in the dark/Brewed Awakening = This treat with many alliases is just a standard Cup o' Joe with a shot of espresso dropped in
That's all the standards I can think of... if there's anything else I forgot, please add to the list