A lot of things are the same between the two games -- talents are very similar, and there are a lot of comparable mechanics and spells (DoTs, healing, and aggro, of course, all play a role in AoC as well as in Azeroth). But there are a lot of differences, too: Age of Conan's combat is based on real-time, which means you actually press a button to strike, rather than just setting a target and going to town. Instances play a different role, too -- you start out in a private instance, and can level in a world by yourself for a much longer time than in World of Warcraft. And Funcom has put in quite a few things designed to pull us away from WoW also: mounted combat, a deeper guild system, player cities, and some more PvP mini games.
Of course, even if you do go to play some AoC, Wrath of the Lich King will probably bring you back to WoW anyway -- as fun as killing stuff in the Hyborian Age is, it doesn't hold a candle to meeting Arthas Menethil, in our humble opinion. But if you've heard about Age of Conan and are wondering what the difference is, Massively's guide has you covered.