Inspiration vs Motivation
As a leader of learning (e.g., teacher, instructor, coach, facilitator) you can inspire your learners but you cannot motivate your learners.
You can own the inspiration but the learners own the motivation. That’s splitting hairs you say because they’re basically the same thing.
Think of extrinsic and intrinsic motivation. To be extrinsically motivated somebody rewards or punishes you and you in turn are motivated to behave a certain way. To be intrinsically motivated you find the motive yourself to behave in a certain way. The end product for both intrinsic and extrinsic motivation is that you motivate yourself but the starting point for each is different — the influence that leads to the action is different (i.e., in the former it’s a reward or punishment, in the latter it’s something within you).
Reward and punishment are two forms of the exact same thing — getting people to do what you want them to do when they wouldn’t have done it otherwise.
For learning — which could be defined as a relatively permanent change in behaviour — to happen it should be something the learner wants to do, not feels he/she has to do.
We erroneously call some people good at motivating others to learn when what they truly are is good at inspiring others to want to learn by themselves. A good motivator uses the carrot or the stick to get the desired behaviour. A good inspirer finds ways to tap into the learner’s inner drive, often by connecting emotion and personal interest to what needs to be learned.
You can inspire a learner to motivate him or herself to want to learn but you cannot intrinsically motivate a learner. Learning is best done as an active, not a passive process.