As it comes from my experience I heard the waterfall model name specualtions pretty often. Some people call it it linear and incremental, others think it's sequential, and it's a pretty much of people call it iterative. So what is correct?
As the history says, originally waterfall model (and the termin) was mentioned (in-directly) by Dr. Winston W. Royce in 1970 in the article "Managing the Development of Large Software Systems: Concepts and Techniques". Also, some people believe that the originator of waterfall name and concept was Barry W. Boehm, also in 1970. I never found any approvals for this fact (maybe I didn't look good? The only thing I know about him is that he came up with the spiral model), but I read the Winston Royce's article.
Actually, Winston Royce never used termin waterfall, but came up with a nice diagram, with "from up to down" layout, that's why a lot of people, who briefly went through his article thought that it looks like "waterfall". His original model was different from what the most people talks about now. The biggest difference seen is a feedback possibility between the stages. More than that, the model what the most people suppose to be waterfall was very briefly described by him and as a concept only, because he was proposing changes to it, turning the model into iterative (using his own terms) or spiral model (a lot of people suppose that spiral model is the nearest one to Royce's iterative model).
So, as it comes, there is no waterfall model, but only the concept of what is it. And the concept is very blured, with the only important and clearly stated detail is that the process is going steadily downwards. It is a purely sequentially ordered model. With the only Parent - Child (Up - Down) relationships, with no way to feedback.
Well, now speaking about terminology, the waterfall is more close to the core concept of pure model, when spiral, iterative and incremental models are the pure waterfall (if I can say so) with applied changes to it. What is linear or sequential models sometimes? Most likely these are synonyms, aren't they? Like spiral model adds an iteration and becomes the same as iterative.
What I really would like to see someday is a list of the main changes to waterfall concept (it's more concept than model) with all these similar-named models grouped altogether. If someone can help me on this, I'd greatly appreciate it.