How did the two climbs differ? Tommy and Kevin free climbed the Wall, which means they went up using just their own physical skills and considerable climbing talents. The ropes and other protection were in place to prevent them from falling, but didn't aid their ascent in any way. This is a much more difficult way to climb, and many thought it was simply impossible to go up the Dawn Wall in that fashion.
For a look back on the climbing scene from 45 years ago, check out this amazing clip. And big thanks to the Adventure Journal for sharing it with us.