Iced coffee is hot-brewed coffee that has been allowed to cool and then served over ice. This usually takes a couple of hours although you can speed up the process by chilling in the refrigerator. Another quick-brew option is to use the proper portion of coffee for your carafe but half the volume of water and brewing directly over ice. Iced coffee tends to exhibit a flavor profile shifted toward sweet, fruit and brightness notes.
Cold brew (or cold press) is a process where the coffee is steeped at room temperature instead of using hot water. Medium to coarse-ground coffee is steeped in room temperature water for 12-24 hours then filtered for use. By using a greater amount of coffee you can create a concentrate that you serve over ice with water and/or milk to regulate the strength. Cold brew tends to present itself as smooth and mellow as this method does not extract so much fruit and brightness.
And the Winner Is?
Generally it comes down to personal preference, especially regarding taste profile, light and brighter versus smooth and more body. Cold brew is often more expensive at your retail cafe because of the extra coffee and time to prepare but you do get a bit of a caffeine bump. If you're making at home why not try making both?