in a way, they are the same.
although:
I give "present" to my love ones (family, wife, children) while,
I give a "gift" to my colleagues, friends and co-workers.
therefore, we give "presents" to whom we love or to whom we have an affection with.
sometimes, a "gift" can also be a "reward" in which it can't be interchanged with "present".
ex: "this is my gift for having earned a thousand points thru my credit card." ("present" can not be used here).
:)