The term Research Unix first appeared in the Bell System Technical Journal (Vol. 57, No. 6, Pt. 2 Jul/Aug 1978) to distinguish it from other versions internal to Bell Labs (such as PWB/UNIX and MERT) whose code-base had diverged from the primary CSRC version. However, that term was little-used until Version 8 Unix, but has been retroactively applied to earlier versions as well. Prior to V8, the operating system was most commonly called simply UNIX (in caps) or the UNIX Time-Sharing System.
Because both the early versions and the last few were never officially released outside of Bell Labs, and grew rather organically, Research Unix versions are often referred to by the edition of the manual that describes them. So, the first Research Unix would be the First Edition, and the last the Tenth Edition. Another common way of referring to them is Version x (or Vx) Unix, where x is the manual edition.
All modern editions of Unix (excepting implementations from scratch like Coherent, Minix, and Linux, usually referred to as Unix-like) derive from the 7th Edition.
First edition of the Unix manual, based on the version that ran on the PDP-11 at the time. Unix was actually 2 years old at the time and had been ported from the PDP-7 to the PDP-11/20 in 1970.
First Unix written in C. It also introduced groups. Number of installations was listed as "above 20". The manual was formatted with troff for the first time.
First Unix to see widespread distribution outside Bell Labs, as well as the first to be ported to non-PDP hardware. May 1977 saw the release of MINI-UNIX, a "cut down" v6 for the low-end PDP-11/10.
The ancestor of all modern UNIX systems and the last release of Research Unix to see widespread external distributions. Merged together most of the utilities of PWB/UNIX with an extensively modified kernel with almost 80% more lines of code than V6. In February, a port called 32V was made to DEC's VAX hardware; 32V was the basis for 4BSD.