When learning How To Rock Climb these are the more common styles or types of rocks climbing.
Bouldering - climbing low routes that are relatively safe without the use of ropes. Components for safety may include a pad of some sort at the base of the climb and/or someone on the ground to direct a climber away from potential hazardous areas.
Top-roping - an anchor at the top of a route provides a point to run the rope through as it is tied from climber to belayer. The belayer then is responsible for making sure the climber does not fall very far. This is considered the safest type of rock climbing, and is ideal for the newcomer.
Traditional climbing - the climber or climbers place any and all required safety gear as they climb and remove it as they progress, when they have completed the climb, nothing is left behind. This form of climbing does not deface the natural rock and leaves no trace after the climbers are gone, therefore ecologically it is the best form of climbing, though perhaps not the safest.
Sport climbing - in sport climbing any and all safety gear is permanently attached to the rock along the determined span or route(s).
Scrambling - in scrambling the climber basically uses his hands and feet to accomplish a route. Scrambling is generally a free solo style, however protection and rope are used on advanced routes that are "technically", normally scramble routes.
Free climbing - a form of climbing where the climber may use safety gear as a backup to prevent injury, but only uses their strength, balance and ability to actually perform the climb. This is in contrast to aid-climbing where the climber utilizes the gear to help reach the summit.
Lead climbing - The leader will climb from the start point with his rope as the second climber belays him. He establishes or utilizes intermediate safety points as they progress through the climb. The second climber catches up to the lead climber at every point, and thus they belay each other as they go.
Aid climbing - as the climber ascends the route they place gear at intervals to assist or "aid" the climb. In this type of climbing the gear and rope may be used to directly help the climber reach each point in the climb.
Free soloing - the climber climbs alone and without the use of any safety gear. This type of climbing is probably the most dangerous and potentially lethal.
Rope soloing - a form of climbing where the climber starts a route with the rope tied off allowing them to belay themselves as they go. This could be done as free climbing or aid climbing or even a combination of the two.
Solo aid climbing - this type of climbing usually involves a harness and at least some safety gear or protection but no rope. The climber will free climb as much as possible and only use safety gear as required by the circumstance. The climber may or may not use the gear to "aid" in the climb.
Deep water soloing - this is a form of free soloing where a climbers route on the rock face is over a body of water deep enough to protect the climber from serious injury in the event of a fall.
Simultaneous (simul) climbing - this is climbing where two climbers progress up a route at the same time. Much like lead climbing except the roles may reverse at any given time. A form of traditional climbing, usually one climber places the safety gear and the other collects it as they go.