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.