Examples of a cascade (left) and a cataract (right)
Now that we've explained the terminology, let's examine some different types of waterfalls. The most basic and recognizable type of waterfall is the plunge waterfall. This happens simply when a river spills out water over a ledge, and the water descends vertically without coming into contact with any of the rock on the way down -- it just crashes right into the plunge pool. This type of waterfall would take longer to retreat, since the hard rock over which the water is flowing is more resistant to erosion.
A block or sheet waterfall is formed from a wide river -- when the water spills over the edge, it looks like a big sheet, especially if the flow isn't broken by any stray rocks protruding from the back-wall. A block waterfall is usually wider than it is high. Similar in nature is the curtain waterfall, which is simply taller than it is wide, but still looks like a long sheet.
Horsetail waterfalls are in constant or semi-constant contact with rocks, which may erode faster than other types because of constant runoff.
Because the geography of the land is never limited, a waterfall can be one of these things or have any combination of them. For instance, a punchbowl waterfall might descend into a small plunge pool, but the plunge pool might quickly lead to another ledge where the water descends as a plunge waterfall. These waterfalls are generally called tiered. There are seemingly endless possibilities, which is probably the biggest reason people look for and are interested in new waterfalls.