These are some working definitions, based on my experiences in astronomy:
Postdocs: researchers with a a PhD who generally have fixed-term contracts. Generally these positions are full-time research, though some may include teaching components.
Research assistants: researchers, typically without PhDs, working in a group/lab. This is frequently a synonym for undergraduate or graduate students, or interns. It can also mean people with technical skills who are working in a group/lab but not working towards a degree.
Research scientists: Non-tenure track reseachers, often with PhDs. Their positions may be fixed-term or indefinite.
Visiting scientists: Researchers whose primary affiliation is with another institute. They may be fixed-term visitors (e.g., faculty on sabbatical at another University) or frequent but non-constant visitors of an institution. Their salary is often paid by their primary institute, unless the host institute has provided funding.
