Generally speaking, natural waterfalls come in two types - plunge and cascade. Everything else that appears in the "form" is there to narrow down the shape of the waterfall for better identification. This is, of course, a human conceit based on our need to put a label on everything. No waterfall gives a hoot about the labels that we apply to them.
Dams fall into a category of their own: Some are a simple concrete wall, others still have at least some remnant of the waterfall that existed before the construction of the dam.
A plunge waterfall pours over a lip and drops straight down without making contact with the rock behind it. Of course, there are exceptions to this rule (there always are) such as terraced falls.
Unlike a plunge waterfall, a cascade maintains contact with the ground over which it is flowing for all or most of its descent. Many cascades begin or end with a plunge.
A curtain waterfall is one where the maximum width is noticeable wider than the height of the waterfall.
A ribbon waterfall is one where the height of the waterfall is noticeably greater than its maximum width.
A terraced waterfall is one where several segments of the waterfall are separated by "Terraces" or level
steps. For example, Albion Falls is a Terraced Classic Cascade.