Well, it might be, but you can inspire an idea (a muse for art etc), without offering any motivation at all.
You can motivate a person to do something (offering a bribe/promotion etc), but you need not have been the inspiration for the initial idea.
I think both inspire and motivate are common in the sense of encourage or stimulate.
However, in "A inspires B", A may not know that B is inspired by him, or A does not purposely encourage B.
In "A motivates B", A usually is in a superior position to B (e.g A is a manager and B his worker) and A encourages B purposely so that he can benefit from a motivated B, who may become more loyal, diligent and devoted to his job.