What's the difference? It's quite simple. In the South we call it chicken fried steak, meaning steak that is breaded and fried like chicken. Outside of the South, in the cities, and for some reason in many restaurants, it's called country fried steak, as if only people in the country would fry stuff.
I prefer people use chicken fried steak, as country fried steak doesn't really make sense, but whatever. It's a classic Southern food and it's quite delicious. If you haven't tried it I would highly recommend it. However, stay away from the pre-made crap that you buy in the store and just heat up. It needs to be prepared by hand.
Traditionally, home-made mash potatoes and white gravy is served with chicken friend steak as the gravy is used on both the steak and the potatoes. That's usually it though some would add a side of a corn, green beans, or a roll. It's delicious.