I know I'm resurrecting a dead thread, but considering I'm going through a similar process right now I figured I would leave my 2 cents.
I would caution against the advice of individuals who say "don't worry about it, let your resume explain your position", at least in reference to non-academic positions in the US. You should have two resumes/CVs, one for academia and one for everything else. In academia the recruiter or PI should understand what "Research Assistant" or "Graduate Research Assistant" means. However, in industry some large companies hire 3rd parties to do their recruiting. In the US the average time for a recruiter like this to read a resume is 5-7 seconds. While this website might not be representative of all recruiters, it does emphasis the importance of your position title. Here is an excerpt, emphasis is mine:
- Level. If I’m doing a VP level search and your title is “manager” and you have never been a VP – goodbye. There are exceptions to this, but again it is the 80/20 rule. Again, clients pay me to find them the perfect fit. It is generally way too big of a jump from manager level to VP level, all other things being equal. It works the other way too. If I’m looking for a manager and you are a VP – goodbye. I know you are qualified to do a manager level role, but it is clear you have grown past. Most clients and recruiters aren’t willing to take the chance that when a VP level position comes along that you won’t be gone. Less than 5 seconds to figure out.
Accordingly, I think it is completely feasible that even if you have your PhD and multiple publications the recruiter could see an "Assistant" Research applying for the "Senior" Research position and immediately reject you simply because of your position title.