Many of us tend to use the two words interchangeably in most contexts. Of the two, present is the more informal. The two words are used with things given to other people without expectation of return or compensation. It is not uncommon to hear people say, I gave him a gift/present on his birthday. Both the sentences are grammatically acceptable. Careful users of the language make a distinction between the two words. A Gift tends to be much more valuable than a present. It usually passes from the rich to the poor, from the high to the low. A present, on the other hand, passes between equals or from the inferior to the superior. • The children brought a present for the Minister. • I gave him a pen as a present. • The foundation is planning to gift the land to the society. • He made a gift of two million dollars to his old university. The word gift is also used with the inborn talent or skill that one has. It is because God is believed to have given us these things. We are getting something from a superior being. Picasso had the gift of painting. M.S has the gift of singing, etc. We do not, in these cases, use the word present.

both of them has the same meaning

gift = present but no one says "birthday gift"