Are PhD Students and PhD Researchers the same thing? Similarly to how a Postdoc researcher is a researcher, I think that a PhD student should be considered a researcher. Especially when:


A salary is obtained for the research that is done as part of the PhD studies. Per definition, I would say that students pay, they are not paid.
A research master has been studied before and there are no lessons, classes, exams, etc. So in fact the person is not a student, but "at least" an "apprentice".


I know that naming things in one way or another may not make a big difference for those in academia that read the CV, but it may evoke different ideas for those out of academia that read it.

AFAIK, they are absolutely equivalent, even if one is more used than the other (mistakenly, IMHO). Nevertheless, I would like to get confirmation, if possible from an authoritative source (like a dictionary for titles), and at the same time I think that the question may be useful for many people.
I don't see the point in your distinctions in either bullet. Some students get a salary, some do not. Neither of these is determinative of whether a student is a researcher. Not every PhD student did a Master's degree before the began their PhD studies. I certainly did not. 

Why do you care if PhD students (who I agree do "research") are "researchers" or not? Of course they are researchers because I think that anyone who does research is a researcher (paid, student, or otherwise). Are you looking to validate your ego, to overcome an officious rule that says that only "researchers" may do some thing or other, or are you looking for something else? Except in a few places, titles matter little. If titles matter where you are, then find the law or bureaucratic codes that define "researcher" and follow them. If you don't like the answer you find, you can either live with that, find a workaround, or fight (presumably through a legislative body if that place has one) for change. You haven't given us enough detail about why you care for us to helpfully answer your question.