Controller vs Micro controller?

In pure control theory, everything is a mathematical entity. So a controller is a mathematical entity that realizes a certain transfer function (or a certain time-dependent behavior, if there are multiple inputs or outputs involved).

A microcontroller is a term for a chip that contains a microprocessor core, memory, and peripherals, that can run stand-alone but for needing to be mounted to a board. In other words, it's what would have been built onto a 200mm x 200mm square board in 1978, and would have cost $200 in parts (in 1978 dollars), -- only microcontrollers hawe ten to one hundred times more of just about everything, and you can get them starting at about $0.50 in quantity.

To either confuse things or clarify:

You can take a microcontroller and you can implement a controller on it, using the microcontroller's peripherals, and make it part of a physical, real-world control system. This will rapidly lead to you being whacked upside the head with the difference between theory and practice, when you first turn your system on expecting good stable behavior from your plant.

But you cannot take a controller from control theory and implement a microcontroller inside of it. You could use some of the same language and implement a model of a microcontroller (with much cursing and head-scratching from both your local control theorists and your local computer scientists). But you couldn't realize a physical microcontroller.