What is the difference between an IC50 and an EC50 and an ED50?

The differences are just nomenclature, and not conceptual.

"EC" means effective concentration, and is used for dose-response curves that go up hill. Sometimes it is also used for a curve that goes downhill. 

"IC" means inhibitory concentration, so is used for dose-response curves that go downhill, because the drug inhibits a response. 

In both cases, "C" stands for concentration. In some experiments, you vary the administered dose, but don't know the effective concentration. In these cases, the midpoint is called the ED50.