Is a waterfall considered a type of erosion?
Waterfalls often cause erosion, but a waterfall is not a 'type' of erosion in itself. The power of the water, as it hits the bottom, picks up dirt and sand that act as abrasives, grinding away at the rock. PBS in the United States has recently shown a very impressive documentary about the formation of Niagra Falls and the way that erosion facilitated the creation of the falls.
It creates what is called "headward erosion".