Ted Williams' War Service

I’ve read that Ted Williams was both a stateside flight instructor during WWII and that he saw also saw action as a fighter pilot.
Which is it? Or is it both?

He saw action, both in WWII and Korea. He rejoined to go to Korea.

Technically, Williams was in the Marine Reserves during the Korean War and he was called up to serve there.

He enlisted in the Marines after the 1942 season ended. He had received a deferment from the draft because he was his mother’s sole support.

He then served in the Korean War, flew 39 missions and received three air metals.