Sometimes you simply make minor tradeoffs to gain simplicity. If your whole site is done using a certain technology then you just continue using it even for static pages where it would not always be mandatory (the processing time in this case is negligible).

Also many projects are done by larger teams, where the people doing the content do not even have much knowledge of how to write a static page in html. Just giving them a way to handle things like “about” pages as everything else will be simpler.

Then there is the issue of translations. Most good CMS can handle this in some way, most frameworks have some feature for this or at least there are plugins. With static pages this becomes difficult to handle. So if you need several languages or plan to do so some time in the future the option for static pages is mostly gone.

So as a conclusion I think if nothing else, then it’s mostly about simplicity of the project as a whole. Have everything work the same way with the additional advantage of getting some extra flexibility for future improvements.

A CMS means more than just storing your content in a database. The usual purpose of a CMS is to allow users to make changes to a website without requiring any technical expertise. It allows these users to log into a friendly user-interface which allows them to write, modify and publish content without any knowledge of HTML or any additional tools like an FTP client.

Also, not every CMS uses a database. It is completely possible to create a CMS which is backed only by flatfiles. I once wrote such a system myself.

To answer your question: When you use a CMS backed by a database, your website is both database-driven and CMS-built. But you can have a database-driven website which is not using a CMS, or a CMS-built website which doesn’t use a database because the CMS doesn’t use one.