You are correct about the difference between freeclimbing and free soloing. Honnold had nothing to save him if he fell. Caldwell and Jorgeson had a rope and gear and a belayer to catch them if they fell, but they climbed their whole route without pulling on gear to help them climb.

They climbed different routes. The Dawn Wall route had not previously been free climbed, it had only been aid climbed before (meaning climbers pulled on gear to help get through the most difficult sections). Honnold climbed a route called Freerider which is easier than the Dawn Wall but still very very very difficult.