They are both the same, normally 'gift' implies someone has given something to you without expecting anything in return, 'present' is commonly used on Christmas where people EXCHANGE gifts, but both can be used.

Gift is often more impersonal than a present. For example, a rich person might give money to a deserving organisation as a gift, or a valuable painting to an art gallery as a gift. Companies might offer a 'free gift' to new customers, or a children's magazine might come with a plastic toy attached as a 'gift' for the readers. These are not 'presents', because they are not personal. In personal situations, such as buying something for a friend for their birthday or wedding, we tend to use 'present'. Gift is also possible, but it feels less personal. For example, department stores may have a section called 'Wedding gifts'.