What is the difference between learning the Buddhist way and simply learning from life? What is different about being a Buddhist than an atheist?

As far as I can tell, "western" thought is a mix of different philosophical approaches that can be applied to life with a dose of common sense: ethics, rationalization, self, society, abstraction, belief, existence, nature... there's place for everything in "western" thought, one just needs to look in the right places.

I've heard good things about Buddhism, but everything I've read about until now is just a different way of saying something that I've heard elsewhere. Different words, a different language.

Does Buddhism recommend itself as the best approach to reach enlightenment, or can this fulfillment be achieved outside of Buddhist schooling?

Or more subjectively: Why should a person follow Buddhism instead of something else?
The main difference is time. Buddha shows the way in simple instructions, so that you don't have to discover the path to enlightenment by yourself.