Don't confuse the two, because they're not the same! In fact, they don't even taste the same. Iced coffee is brewed the same way as hot coffee, heated water is steeped over coffee grounds and dripped into a vessel, then allowed to cool and poured over ice. Conversely, the cold brew or Toddy method is steeped using cold or room temperature water and can served cold or heated and served hot. This method takes much longer than the iced coffee method, twelve-plus hours!
So why would anyone employ a method that takes so much longer? It's simple really, the taste. Cold brewed or Toddy coffee ends up being sweeter and less acidic. I'm not a chemist or even a brewmaster, so I won't pretend to know the nuts and bolts of why this is, but suffice to say, hot water causes different chemical reactions which ultimately alter the taste.
How can I cold brew? You can't use your normal drip system. I have yet to see a normal coffee brewer that allows you to turn off the heating element, or not preheat the water during the steeping process. In addition, hot brewers drip way too fast! As I said before, most cold brew methods take twelve hours or more... your Mr. Coffee brews in 10 minutes! There are some methods that are much shorter, try them both out and let us know your thoughts.
Below are few links for DIY and ready-made/retail cold brewers. Before you take the dive and make or buy a Toddy system, go to a local coffee shop and try a Toddy for yourself. In Denver, I recommend Crema Coffee House, they serve a Toddy made from Huckleberry Roasters beans... and it's fantastic! That's the cup that made me a believer in cold brew/Toddy.
Bruer - Currently pre-order only - fairly inexpensive
Not DIY, unless you're a chemist. :)