What are difference between climbing a rock and a wall?

It is as simple as what you are climbing.

Wall climbing is an indoor way to learn about climbing, practice, train, socialize, and compete. This is a more modern way to expose people to climbing in a controlled environment.

Rock climbing is the original activity. It takes place on real rocks. You can climb whole mountains, single pitches at a cliff or even boulders.

Get out there and climb something! :)