There should be no difference in terms of what resources are available to the R session whether you use RStudio Desktop or RStudio Server. That said, if you're attempting to run RStudio on a Windows machine, you're limited to RStudio Desktop as RStudio Server only runs on Linux machines.
RStudio Server Pro is useful when you have a cluster of many machines, and want to control where new R sessions are spawned (so that new R sessions can be spawned on machines with relatively lower load). However, once the R session is launched, it behaves just as it would if you had a locally running instance of RStudio Desktop.
This doesn't imply that RStudio Server will automatically distribute computations across nodes for you; rather, it can help distribute newly launched R sessions across machines so that each machine is utilized as effectively as possible.