When rock climbing, what is the difference between lead climbing and top rope climbing?

The difference between lead climbing and top rope climbing has to do with the location of the rope when the climb is started. In lead climbing the rope begins at the bottom attached to the climber as well as the belayer. The climber must then bring the rope from the bottom of the route to the top by clipping into a series of quick draws that are generally placed 10-15 feet apart. If a person were to fall while lead climbing, they would be caught by the last quick draw they clipped into. When top rope climbing, the rope is already at the top of the route. This means the climber must tie into one side of the rope while their belayer must clip into the other side of the rope. As the climber ascends higher up the route the belayer must take out the slack of the rope as opposed to lead climbing where the belayer would be giving slack. When a person falls in top rope climbing they will only fall a short distance as the rope is already clipped in above them at the top of the route, so how far they fall will be determined by how much slack the belayer has not taken in.