This is a very fine ground coffee that is packed into a portafilter and inserted into an espresso machine. Water that is heated to 190-197 degrees Fahrenheit is forced under 8-10 atmospheres of pressure through the portafilter of fine coffee to produce --viola!-- 1-2 ounces of espresso. And do not feel bad about calling someone out when they say, "expresso", because there is no "X" in espresso.
Hint A good way to tell if your espresso is of high quality is the color and consistency of the cream. If you add sugar, it should sit on top of the cream for 15-30 secs.
A latte is something North Americans have made popular. In Europe, a latte would tend to be considered something you would serve to your children. When made properly I consider a latte to be a delicious drink. Many people confuse the latte with the cappucino. A latte is espresso in combination with steamed milk. To give you an idea of ingredient ratios, a 16oz. drink would be 2-3oz. of espresso and the rest steamed milk.
Hint: I consider a good latte to be a "blended" drink. A good barista will incorporate foam, steamed milk, and espresso together giving the drink a blended taste and a marbleized texture.
This drink is often confused with a Latte, but in essence they are different drinks. The common cappuccino is made in 1/3 proportions. This means a proper cappucino is 1/3 espresso, 1/3 "steamed" milk, and 1/3 "frothed" milk. The espresso and steamed milk are poured together and the frothed milk is scooped on top. This drink is very subjective in my opinion, and can be ordered several different ways.
Hint: I think this drink is a good test of how good a barista actually is, and be forwarned if you do not like formy-ness order a latte...
Cafe Au Lait
This one is easy and straight forward. 50% Dark Coffee: 50% Steamed Milk.
Hint: The only factors here are tasty coffee and fresh milk. Don't let them use milk left over from their last drink. You want unsteamed, fresh, cold milk.
I hope this answered your question.