A microcontroller is like a super tiny computer that typically runs a single program. With rewritable flash memory the modern microcontroller boards we stock like Arduino can be reprogrammed many times to experiment and play. The boards provide all components to support the main processor chip and connecting external components like sensors via headers or solder holes is simple.
Robot controllers are specialized microcontroller boards that normally include motor drivers and provide for easy connection of servos.
Input-Output IO Boards allow you to offload the processing of input from sensors or output to other devices and allow for connection of many more devices than a microcontroller may support by itself.