I would only use "turn to the right" if I wasn't talking about driving. If someone was standing in front of me and I wanted them to rotate 90 degrees (or so) then I might say "Now turn to the right". In a car, you might tell someone to "turn the [steering] wheel to the right" which would have the obvious result of making the car change direction but you wouldn't only do that to get them to actually turn a corner. They could turn the wheel to the right simply to swerve to avoid something in the road.
If giving driving directions, I would simply say "Turn right".