What is the correct term for a PhD student who does entirely research and is paid through third-party funds?
One can see that sometimes people doing a PhD call themselves a Research Associate or Research Assistant (in a very few cases also Research Fellow). I am looking for clarification regarding which term would be appropriate and also why the others are not.
I can't find a clear definition. If this is country dependent I would like to know this for the UK and Germany.
Answering in the sense of the German system and as I understand it and have experienced it:
Research Assistant: Someone holding a BSc (often a MSc student working alongside their studies)
PhD student/ PhD candidate/ Doctoral candidate (Doktorand) (used interchangeably): Someone enrolled for a PhD program at a University. Usually not anyone can enroll. You will have to have supervisors supporting your idea and submitted a qualified research proposal.
Research Fellow (Wissenschaftliche_r Mitarbeiter_in): Scientist with a MSc or PhD, usually a fixed-term contract through a third-party funded project. Often PhD students also hold a position as research fellow (e.g. opposed to receiving a stipend).
Research Associate (Wissenschaftliche_r Mitarbeiter_in): Scientist with a MSc or PhD, same term in German. In English, the difference apparently refers to the position being a permanent one and independent of third party funding. See What's the difference between a research associate and a research fellow?. This is a less likely context for doing a PhD, but possible.
Post Doc (Wissenschaftliche_r Mitarbeiter_in): Referring to a scientist with a (nearly) completed PhD. Usually fixed-term and running on third-party funding. In the German academic system, the salary is usually the same as for research asscociates/fellows. They all count into the same category (Wissenschaftliche_r Mitarbeiter_in).
Regarding the initial Question: In German academia, you can technically be both at the same time: a PhD student (referring to the status of your studies) and a research fellow (referring to your status as an employee). During my PhD, I was enrolled as PhD student at one Uni and employed as a research fellow at another.
How about "PhD student"?
Since you also asked about Germany: in German you can call yourself "Doktorand" or "Promovend". But also in Germany, "PhD student" would be perfectly fine.
If you want to leave out the "student" part, you might call yourself "PhD candidate".
Be careful to avoid calling yourself something you are not (e.g. "Dr."), since particularly in Germany that might be illegal.
I'm not sure if it is the same in the UK and Germany, but in the US, "Research Assistant" typically means a person is being paid by a professor (typically using 3rd party funds) to work on their project, while "Research Fellow" typically means the student is being supported directly in their studies and/or research.
Fellowships are thus generally more prestigious, since they are a direct recognition of the student's value and potential by an organization, whereas assistantships simply mean that a particular professor thinks the student might be a good worker for a particular purpose.
Note that these titles are somewhat orthogonal of the question of being a Ph.D. student, as they are essentially describing one's "job" and means of support rather than one's educational program: a Masters student may also hold them, and a Ph.D. student may also hold other "job" titles (e.g., "Teaching Assistant", or even none at all).
In Germany, the payment (be it from 3rd-party sources or not) usually comes as a salary for an employment. That position is typically called wissenschaftlicher Mitarbeiter ( research employee ).
You should note, though, that the "only research" part is not included in that title, as there is no real distinction to teaching duties, as it exists, for instance, with "RA/TA".
I see that this question has been inactive for almost two years, but I notice the asker was specifically interested in the UK, and none of the answers cover that country specifically.
From my last three years of experience in the UK academia, those two positions are fairly well defined, and refer to the following:
A Research Assistant (RA) is typically neither a PhD holder nor a PhD candidate. These positions are aimed at people holding a Master degree in the relevant field, and are common in short, 1-year, research projects (such as feasibility studies). They do not count for direct progress towards any degree (but could result in publications and therefore straighten one's PhD application in the future). Additionally, they are typically one pay grade lower than the Research Fellow positions.
A Research Fellow (RF) is what one would informally call postdoctoral researcher (or just post-doc). These are typical positions one would aim at after their PhD (and usually encourage PhD candidates close to finishing to apply as well). They typically rely on funding from longer projects, and last for 2-3 years. They also do not count for direct progress towards any degree (as the holder is expected to have a PhD, the highest possible degree in the field, already), but are a logical and expected step for a young career researcher aiming at a permanent academic position. They are also better paid than Research Assistant positions, being one pay grade higher.
For immigration purposes, universities will always have the ability to sponsor non-British applicants and support their immigration application for RF positions, while some universities and some positions are unable or unwilling to do that for RA positions. (This might be restricted to sponsoring EU-immigration, unsure about this bit).
A PhD student, PhD candidate, or just doing one's PhD are all valid terms to refer to somebody working towards obtaining their doctoral degree, regardless of their funding source. (Sometimes even just "I'm a PhD" is used, but that's common more than valid in the strictest sense.) Additionally, PhD students doing only research, as opposed to having some teaching duties attached to their contract or funding, are often times referred to as lucky.
I use the word typical a lot in my descriptions, as exceptions do exist, and I was one of them, but the details go far out of scope of this question.
In Germany and Spain, if you're a PhD student who gets paid via assisting professors in their projects, typically the position is regarded as Research Assistant. I rarely see who wrote it down in CV as Research Fellow, while research associate sounds more of a postdoc.
