Trophies - How Similar Are They To Achievements?

With the birth of Xbox 360, Microsoft introduced Achievements. This changed the way people buy and play games period, people would play games multiple times just to get every last achievement, some people would buy games they wouldn't usually buy just for more achievements, and others would go hunting in that bargain bin for games they might have passed on just to get their gamer score where they want it. Microsoft indeed changed the game with Achievements, so much that Sony had no choice but to implement their own reward system, So here came the birth of trophies. But what are the main differences between Achievements and Trophies?