Sure: Koehler is usually improperly applied, using compulsion. Koehler as practiced by Koehler is a very very slow method of training. Put the dog in a sit, put him in a sit again, and again, until he learns to sit.

Ellis style is all about letting the dog decide his actions, and then rewarding it when it makes the choice you want. for instance, to teach a pup to sit, we lure the dog into a sit using a treat. when he sits, you mark the reward with a word (some people use clickers) and then treat. You end up with a pavlovian response, where when the dog hears "yes" or "good" he expects a treat, and gets excited. After awhile the dog will start sitting on his own, and you mark/reward that. Later on you can add in the command, when the dog is performing the action on its own.

The difference between the two methods is that with the ellis style, you end up with a dog that WANTS to work, and looks to you for direction rather than being dead inside.

I could go on more, but don't really have the time.