What is the hierarchy of rank of job titles in research science?

Answer 1

I will start the answer process by qualifying it: these are geared more for academic positions and each institution can change the wording slightly to mean very different things.

Typically:
Top Position - President of the University (mostly raises money and makes public appearances; sometimes heads active research lab with a limited amount of oversight)

Chancellors - mostly administrative

Deans - mostly administrative though can also head active research labs

Faculty - The top faculty ranks can be garnished with accolades, but generally are from top to bottom: Professor, Associate Professor, Assistant Professor

Project Scientists and Research Associates / Fellows - Typically PhDs (though sometimes holders of Bachelors and Masters degrees) who have for the most part made it out of the "Post-doctorate" category

Post-doctorates (aka postdocs) - Often new PhD graduates on their first, second, sometimes third post-degree assignments. It's tough to move past a post-doc position due to lots of competition from fellow postdocs and up.

Research / Teaching Assistants - can vary from undergraduates looking to get into research (or at least building a resume) to newly graduated bachelors looking to figure out the next step in life to graduate students (pre-doctorate) who are not Fellows (typically grant recipients).

Research Fellows - a category that typically fits scientists earlier in their career rather than later, often graduate students and postdocs who receive grants to do a particular project or study a particular aspect of a field.

Experiment subjects - not really a job title, though in the Social Sciences human experiment subjects are greatly needed and although somewhat contrived, "professional" subjects can provide better data than novice subjects by not contributing to unwanted noise in the data e.g. instead of pressing "1" or "2" in a 2-possible-answer question, leaving answer blank often giving the research scientist a statistical headache with which to deal.

I hope this helps to get the ball rolling.