Adam - This might be a bit of a rant, if so, forgive me. If I provide all of the pertinant information, perhaps additional questions are not required to achieve understanding.
We (my wife Gail & I) learned that a course or rough edge would cut more aggressively, especially on rope or similar materials. This was because of the rough tips pertruding slightly beyond the edge were acting like the point of a knife, initiating the cut. On the negative side, these rough tips easily broke off creating poor edge retention.
On the other side, a highly polished edge would have greater edge retention, but didn't have the grabby or hungry aggression of the rough edge. The synthesis of these two alternatives was a highly polished serrated edge. This gave the us the advantage of the tips initiating the cut and the highly polished edge, now protected by the extended tooth, increases edge retiention.
We found that there was very little real research (that we could find) on the shapes, sizes, etc. of serrations. We noticed that the combination of two or more scallop sizes seemed to cut more effectively on a greater variety of materials. The one large and one small combination we traced back to pre WWII, both in Europe and the USA. Used in the USA by Popeil mid century and Scott and Fetzer (still today). We refined the size, shape, degree of radius and angle of this particular type of serration and promoted same beginning in 1982. With our current kitchen knives, we are experimenting with one extended tooth to greater increase edge retention on a cutting board.
Each change in a serration creates a different look. Different manufacturers have their own theories (as do we) on what we think will work best, thus the different looks.
As we find that certain refinements improve performance, we will evolve in that direction. I hope that answers your question.
I think serrations definitely have a place. I have found that the serrations give sloping cuts though and sometimes this is a problem. I've heard some companies started making blades with both sides serrated which would cut straight in theory. I'm curious as to your opinions on this.
To be honest, in an emergency I could care less about a straight cut, so when working in a dangerous environment my "Rescue" is my favorite.