What is the meaning of the various postdoctoral job descriptions in the US?
As Jon Custer mentioned in the comments, there are no standards whatsoever, however generally speaking:

&quot;Visiting&quot; is a short-term position (I've never seen a post-doc with this title), probably even shorter than a usual postdoc, probably 9 or 12 months.

A &quot;fellow&quot; is usually a prestigious assignment, it may be a  university, college, or departmental soft-money position. For example, my university has &quot;President's Fellows&quot; although I'm not sure if they are funded specially or if that's just an award. However, nothing stops anyone from calling anything a &quot;fellow.&quot;

An &quot;associate&quot; professor outranks an &quot;assistant.&quot; However, I do not think there is any meaningful difference between &quot;postdoctoral research assistants&quot; and &quot;postdoctoral research associates.&quot; One doesn't outrank the other. Probably, people just try to avoid using &quot;research assistant,&quot; since that somewhat connotes an junior position.