Cold beer soaks grains slowly in cold water. Iced coffee is prepared hot with a standard coffee maker, cooled and served over ice. Certain light floral notes can only be extracted with hot water, so iced coffee tends to have brighter (acidic) and more pronounced flavors than cold coffee. The main difference between iced coffee and cold coffee is how each drink is prepared.
As the names suggest, one is regular coffee that is poured over ice, while the other is cold all the time. While iced coffee is prepared simply by pouring cold coffee over ice, cold coffee has an extraction time of 12 hours with cold water. While iced coffee still has a solid caffeine content, cold beer tends to have more caffeine thanks to its long preparation time. Finally, the flavors are slightly different: iced coffee retains a little more of the acidity of hot coffee and cold coffee has a milder flavor.
When the coffee is ready, you will have to pass it through a special coffee filter or cheesecloth. It's not that unique or that mild, but many coffee drinkers love the intense bitterness of well-prepared iced coffee, and if cooled properly, all of these delicious fruity notes can be trapped in iced coffee.