If you just ordered a caramel latte, you're right, it should have been hot! One can order any of the drinks iced, however, and it's basically the same ingredients but cold. Here's a basic breakdown based on my working in coffee shops through college:
Espresso: Strong coffee brewed from finely ground coffee beans
Cappuccino: Espresso with foamed milk
Latte: Espresso with steamed milk, very little foam
Mocha: same as a latte, with chocolate
Caramel/Vanilla/Gingerbread/etc Latte: same as a latte, with flavored syrup
Caramel/Vanilla/Gingerbread/etc Cappuccino: same as a cappucino, with flavored syrup
All of these drinks are traditionally served hot, but can be iced (cold with ice cubes)
Frappucinos are made with a coffee-flavored mix, ice, and flavored syrups, then blended so they are like a smoothie. They also carry non-coffee flavors
now for extra credit:
Cafe au Lait/Misto: half regular coffee, half steamed milk
Macchiato: Espresso poured on top of foam, no milk
Caramel Macchiato (Starbucks): really not much to do w/ a Macchiato, it's basically a vanilla cappuccino with lots of caramel sauce on top.
White Mocha: same as a mocha but with white syrup instead of traditional chocolate.
Any other oddballs you want explained?