Just watched this video - about motivation. Very interesting, and spookily relevant to the post I put up yesterday about how we communicate with our horses. What I took from the video - controlled motivation is the usual 'method' of training animals, whether it be carrot or stick. Autonomous motivation is where you don't externally motivate (I will hurt you if you don't/I will give you a sweetie if you do) but through understanding of the 'other' you are trying to train, create conditions in which they can make choices and motivate themselves. The latter leads, in people, to all sorts of benefits, such as positive emotions and improvements in psychological and physical health.
Anyway, the video says it much better than I could. And my brain is bouncing about trying to think through how I would explain how this applies to horses! Autonomously motivating a horse is clearly not easily explained, but from my observations, when you link a behaviour consistently with 'carrot' or 'stick' you may get the external behaviour that you want, but you lose the quality, and end up with something rather robotic.
Promoting Motivation, Health, and Excellence: Ed Deci at TEDxFlourCity