I certainly would not disagree with what Sylday says about the existence of specific differences between the two words in varied circumstances. However, my earlier response pointed out that I was referring to 'modern usage', by which I meant the day-to-day use made of the words in speech. If you look under 'motive' in a thesaurus, you'll find 'motivation' as one of the alternatives. By the same token, looking under 'motivation', you will fine 'motive'. The words are, very largely, synonymous.