Motivation is external. Motivation is fleeting; it comes and goes. Motivation pushes people to do things. Doing what motivates us doesn't always leave us fulfilled at the end of the day.
Inspiration is internal. It's a feeling deep down inside someone. Inspiration is sustainable. Inspiration acts as a gravitational pull that moves people closer to their goals. Doing what inspires us leaves us fulfilled.
Look at it this way: People are often MOTIVATED by money. Nobody says their INSPIRED by money. That wouldn't make sense. Money doesn't inspire people with a deep down feeling and it doesn't give someone a sense of fulfillment. Money is just a motivator for people.