Inspire means to appeal spiritually, and to appeal in the sense of a volitional reach for a desired goal or a volitional following of a desired purpose. Motivate does not necessarily mean a spiritual appeal. It can have a similar meaning to inspire, but it can also have a lower meaning of being forced to do something or reach for something. We have a saying "The carrot or the stick". It probably comes from different ways to deal with a horse. The "carrot" is a reward for doing something. The "stick" is the punishment for NOT doing something. You want to reach for the "carrot", but you want to avoid the "stick". So "inspire" means going for the carrot. "Motivate" could also mean going after the "carrot", but it could also mean doing something to avoid the "stick".

Motivate : 1- to be the reason why sb does sth or behaves in a particular way example: He is motivated entirely by self-interest. 2 - to make sb want to do sth, especially sth that involves hard work and effort: example: She’s very good at motivating her students. The plan is designed to motivate employees to work more efficiently .3- (SAfrE, formal) to give reasons for sth that you have stated example: Please motivate your answer to question 5. Motivated - adjective: a racially motivated attack example : a highly motivated student (= one who is very interested and works hard) ............................................................................... Inspire : means to influence, move, or guide by divine or supernatural inspiration. Inspire people means to let people be guided by something divine or Godly spirit. 1 - inspire sb (to sth): to give sb the desire, confidence or enthusiasm to do sth well: examples: The actors inspired the kids with their enthusiasm. The actors' enthusiasm inspired the kids. His superb play inspired the team to a thrilling 5–0 win. By visiting schools, the actors hope to inspire children to put on their own productions .2 - [usually passive] to give sb the idea for sth, especially sth artistic or that shows imagination example: The choice of decor was inspired by a trip to India. 3- inspire sb (with sth) | inspire sth (in sb) : to make sb have a particular feeling or emotion examples : Her work didn’t exactly inspire me with confidence. As a general, he inspired great loyalty in his troops.

I am inspired by your question, but not at all motivated to give a detailed answer. :P

He was alone on the mountain after the hailstorm, and seeing the sky turning blue again inspired him for a new path in life. He hoped that those days of closeness could inspire her some deeper feelings. Whenever he was tired of his studies, he read a Scientist's biography to get new motivation. He turned his life in a continuous struggle against injustice, was motivated from what his parents had to suffer living in XYZ. 'To motivate' implies a relation of cause and effect in a particular direction, guided by the intellect; 'to inspire' is also something with great strength where the effect and the cause don't necessarily belong to the same semantic area; inspiration guides the unconscious mind, so the same cause could give different results on different people, or no effect at all. Sometimes the subject knows he was inspired, but can't describe in which way. Motivation is usually capable of being described by the subject experiencing it.

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