'Motive' is normally used to mean the specific reason for performing a specific action, an incentive, a particular goal or objective 'They ran away to avoid being punished.' (motive = to avoid being punished).
'Motivation' is either a) the act or process of giving someone a reason to do something, the internal and external factors that stimulate desire to do something 'I became a vet so that I could help relieve suffering in animals.' (motivation = the desire to relieve suffering in animals)
or b) the condition of being eager to do something or work. 'Some employees lack motivation.'