Motives and motivations can mean the same thing but are generally used differently. Motives are the reasons given for having done something. I may have several motives for eating: to enjoy the pleasure of taste, to nourish my body. Motivation is the enthusiasm for doing something: if I am hungry, I will eat. If I have motive but no motivation I might go for days without eating.

Theses words are synonyms. "What are your motives to learn English?" "What is your motivation to learn English?" (This example sounds more natural)

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Motive is normally used to mean the specific reason for performing a specific action, an incentive, a particular goal or objective. Ex-They ran away to avoid being caught. So the motive here is to avoid being caught. Motivation is the act or process of giving someone a reason to do something, the internal and external factors that stimulate desire to do something. Ex-I became a doctor to ease patients suffering. The desire to relieve people’s suffering is the motivation to become doctor.