The best response that accurately describes the space race and its relationship to the Cold War is:
"During the Cold War, the U.S. and the USSR battled each other. While this conflict never caused direct conflict, the war played out in other arenas. One of these arenas was outer space. The space race is the term used to describe the race for superiority in outer space."
This response clearly states the context of the Cold War, emphasizes the race for space superiority, and accurately reflects the nature of the competition between the two superpowers without claiming direct military conflict in space.