Buck Woody discusses whether Microsoft R Client really is a client:
Enter the Microsoft R Client. It includes Microsoft R Open, and adds in some of the ScaleR functions, which makes processing data faster and more efficient. And again, it’s a full R environment – you can write and run code, right there on your desktop. But the important bit is that it can connect to a Microsoft R Server (MRS) by seting something called the “Compute Context“, which tells the R environment to run on a more powerful, scalable server environment, like you may be used to with SQL Server.
The naming is a bit of a head-scratcher, to be honest.