There's really no difference. When you say моята майка you are stressing the fact that it's your mom and not someone else's. But you could still use both in almost any context. I would recommend using the short posessives when you are talking about multiple things though. It sounds better to say "Майка ми е лекар, а баща ми е полицай." rather than "Моята майка е лекар, а моят баща е полицай." But as I said if you want to stress that it's your mom you should use the longer versions. "Моята майка е лекар, а твоята е полицай."