Both forms of sport are done outdoors on natural surfaces such as rocks and indoors on artificial surfaces like climbing walls. They are both olympic disciplines and common amateur sports.

With the development of bolted sport-climbing in the 1980s the popularity of rock climbing as a sport increased. Climbing is about going up while being secured by climbing equipment. Bouldering is about going rather sideways without any safety device. Bouldering has become quite popular in recent years. The number of bouldering halls is continuously increasing.

https://en.wikipedia.org/wiki/Bouldering

Climbing has been suggested before but in a different category.