I think there is some misconception here about the different pieces of software and how they interact.
- RStudio Server Pro - the IDE running on a server (access in your browser), commercial version
- RStudio Server Open Source - the IDE running on a server (access in your browser), open source version
- R - the open source language where packages are loaded, code is executed, etc. R has many versions (3.4.3, 3.4.4, most recently 3.5.0) and all should be compatible with the different IDE products
Microsoft has a bunch of software that they bring into this stack as well, but you didn't mention Microsoft, so I'm not sure if any of their products are muddying the waters.
In any case, it is generally not possible to install RStudio Server Pro (the pro version of the IDE in your browser) on the same server where RStudio Server Open Source (the open source version of the IDE in your browser) is installed.
That said, both products require that R is installed on your server. Any version of R will do, and RStudio Server Pro actually allows many versions of R to exist side-by-side, but this usually requires compiling R from source.
I have not mentioned "R server," since that is terminology that we do not generally use. We do require installing R on your server in order to use the IDE products.