Furthermore, the link I posted was written in 1961. What the many people do is to pretend the race to the moon was the race space. For that matter I will make it official, the race to space doesn't end until we reach the furthest particle ejected from the big bag. Is this fair? No, you cannot extend the race to space to match your own accomplishments.
Race to space = Won by USSR
Race to the moon = Won by USA
Race to mars = Not won yet, very likely China or the European union, maybe USA
Most accomplishments in space exploration = that is debatable.
Its a fact man, its not debatable.