Some differences:

Coercion is only one type of control (stick vs carrot). Without modifiers, control sounds pretty absolute while coercion sounds indefinite as to result. And, ironically, in some literature “controls” may refer to a reference set that is NOT manipulated.

It seems proper to me that there should be much diversity in educational methods and goals, as long as both are sufficiently transparent to all parties (after all, parties and education go hand in hand, and parties provide another venue for social control).

I primarily identify as anti-authoritarian and still manage to produce a bit of content. Self-directed cognitive re-engineering is in fact my core topic. I address this in posts like The Meaning of life, Addiction to Irrationality, The beginning of wisdom 3.0, and AHA!.