League of Legends is DotA with training wheels. Basically the original DotA started the genre, and LoL strived to take what they deem "anti-fun" mechanics out of the game. Good examples would be denying friendly creeps / towers, lack of stuns and CC, and the inability to dive towers early in the game.

Another main difference is that League of Legends has scaling magic damage. Because of this, spells are significantly weaker in the early game (due to the fact that you can get items to boost their power as the game progresses). There are no +magic damage items in DotA, so spells are significantly more powerful early game but become less effective compared to auto attack damage as the game progresses.