What is the difference between a controller and a compensator?
As the book's title is control theory; a controller is the general broad name given to any piece of hardware (or sowftware) that aims to control some processes, in your aerodynamics field probably the flight process; by menas of receiving signals from sensors and sending commands to propellers - actuators, and in between is the control hardware or software...

A compensator is a specific control-box-tool to correct (or compensate) some lacking aspect of a system property under concern, such as phase, lag, magnitude etc... It is generally useful as part of a bigger control system, rather than itself being a controller except some simple applications.

Obviously there are many different control system examples in addition to a compensator...