With the proliferation of so many different applications that refer to themselves as web CMSes as well as all the "Web 2.0" applications that allow interactivity with a web site, it's of some academic interest to define what exactly a Web Content Management System is.
My personal feeling as a consultant in the industry is that a "real" WCMS would allow its features to be employed in an existing web site of any appearance without a rewrite of code of the site. Perhaps for optimum functionality you'd re-structure all of the code, but if the system's focus is really content management then you should be able to take any static HTML, anywhere - in an existing page or even in another web application, and easily put that under the CMS's control (though not necessarily without any coding - it's just that it should be an easy, commonly-performed, well-documented procedure). So any software where the normal mode of use is that the system gets to take over the entire page and you have to then modify the system internally, modify templates that came with it or something, to get it to look the way you want isn't a real CMS in my opinion. This is why I wouldn't consider a wiki to be a CMS for example.
The reason why this distinction is merely academic is that the solution to your problem may not be a "real" CMS. Maybe you're starting from scratch with a new site and there's no code rewriting to be done. Or maybe a "web site generator" application with a fixed page or site layout has some special features that make it superior to CMS-based solutions - the needs of a news organization might be better fit by Moveable Type or some other article-oriented or blog-oriented system. Or maybe your web team is looking at an open source application implemented in a technology they're very familiar with, so the price is right and code rewrites won't be a big problem.
If the list of features that CMS products have is dizzying and mostly seem irrelevant to your situation or if the process of deploying a CMS-managed web site seems unnecessarily intimidating a CMS may simply not be the thing you need. Or it may not be the thing you need right now.