In control theory, are manipulated variables and control variables the same concept or is there a subtle difference between them?
Manipulated variables and control variables are the same concept. They are the variables that are used to control the process, e.g. the output of the controller. I'm not sure why there are two different names for the same thing, but I guess it's because the industry and academia often develop different lingo because they have different goals.
The variable that is subject to control is called the controlled variable by some people. It shouldn't be confused with the control variable. I prefer to use the name process variable (PV) instead of controlled variable.
Manipulated variable and controlled variable are not necessarily the same thing. For example, take a water tank level control system where make up water flow into the tank is the manipulated variable and tank level is the controlled variable. There are many other examples besides this one.