Tennis elbow is also known as lateral epicondylitis. Lateral means the outside of the elbow is tender and/or painful. Tennis players are most often affected by this condition because of the way they use repetitive force to swing the racquet.
Golfer's elbow affects the inside (medial portion) of the elbow. The symptoms are the same. The difference is the location and the motions that lead to one or the other developing.
With tennis elbow, the muscles and tendons along the back of the hand and forearm react to overuse. With golfer's elbow, it's the muscles and tendons along the inside of the forearm that are torn or aggravated.
Athletes are much more prone to tennis elbow than golfer's elbow. In fact, tennis elbow is 10 times more common than golfer's elbow. And in either case, participation in the sport for which it is named, isn't necessary. Often there is some kind of repetitive motion or traumatic event affecting the specific tendons mentioned.
Usually, with a little thought and observation, the person can figure out what activities aggravate (and probably brought on) the problem. Avoiding those movements or modifying the activity is often the first step in overcoming the problem. Once it becomes a chronic condition, then tendon inflammation isn't a problem as much as tendon degeneration becomes the issue.
In either case, treatment is needed to restore normal tissue structure and movement.