It's pretty straightforward: ebook is a generic word that encompasses many different digitalized formats for reading.
So yes, that would make a PDF a kind of ebook. But it all depends on how inclusive you want your definition of an ebook to be. I don't think there is any single definition.
The main complaint about pdfs is that you can't edit PDF files easily (it's usually an output format) and that you can't resize the text in a responsive manner (You can only zoom in and zoom out the entire page). That limited its usefulness in smaller devices. In contrast, the epub format and others made it easily to navigate through tables of contents and change text size and global styles. In terms of responsive design, epub was a more flexible format (and indeed, it was constructed precisely for that purpose). PDFs were designed to be viewed and printed in a single size. You can change size to allow it to be displayed on a larger or smaller screen, but it still was built primarily for rendering in one size.
On the other hand, there are lots of tools for producing pdf files (much more than EPUB), and now 9 inch and 10 inch mobile devices are able to view many different sizes without too much pain. Typically though, the pdf tools are office applications and don't allow you to manipulate source code or its styles.
Practically speaking, publishers don't create pdfs except for print copies because amazon doesn't sell pdf ebooks. (But amazon does support fixed layout ebooks, which is similar). But practically speaking, even nontechnical people have access to an application which can read pdf files.
PDFs have been around forever -- and associated with Adobe -- though over time it has been accepted as an OpenFormat and an ISO standard (in contrast to MS Word, for example).
An interesting question (and a frequent subject of debate) is whether ebooks should have embedded fonts or should have the option not to (and use the device's defaults). I might be wrong, but the PDF standard requires the font to be embedded -- which means requiring a fairly sophisticated tool to do this. (Epub just requires the ability to edit HTML).