Many, MANY actors and actresses were typically extremely shy people and performing was a way of bringing them out of that shell (by becomeing “someone else,” in effect.
Stage fright is a case of performance anxiety. Even the most extroverted people can get stage fright in the right circumstances, i.e. actually performing, meeting a date for the first time, being interviewed for a job, etc. It depends on the sdpecific circumstance. It is said that Barbra Streisand, clearly a seasoned perfomrer, would get stage fright before every single performance. The adrenaline rush that comes from that fright, is often what propels a performer to do an outstanding job.