(written from a Production point of view)
20th Century Fox or Twentieth Century Fox, officially the Twentieth Century Fox Film Corporation, is one of the biggest Hollywood film studios. It is a subisidiary of 21st Century Fox, the legal successor of the News Corporation.
The music for Star Trek VI: The Undiscovered Country was recorded at Twentieth Century Fox.
The music for Star Trek was re-recorded at 20th Century Fox.
The company made its Newman Scoring Stage available for the recording and mixing of the music for Star Trek Into Darkness and Star Trek Beyond and was thus included in the movies' credits. While this stage, then known as the 20th Century Fox Scoring Stage, was also used for Star Trek: The Motion Picture and several seasons of TNG, the company was not credited for this contribution.