gymkhana is a form of autocross where the cones are set closer and you have to do some tasks like go around a certain cone twice maybe. or you have to back up into a space... go through a gate backwards. its an obsticle course for cars that challanges the drivers ability to control the car in a demanding environment. its judged on time. sliding the car is used sometimes because you have to turn so tight that the car cant because its steering agle is too high. so its like an even harder autocross.
drifting on the other hand includes some of the same driving but is based around a judged points rule. not time like gymkhana.....
hope that helps. if you youtube gymkhana you will get an idea of what im talking about. its much different from drifting because drift is only a small part that "might" be used when racing in gymkhana. even FWD cars compete in the sport