What is the difference between 'gift' and 'present'?
In your example, there is no difference - the two sentences have the same meaning.
However, the two words are not exact synonyms. 'Present' is generally only used for personal gifts, such as you might give friends and family for birthdays, weddings and so on. You can also say 'gift' in these contexts. But 'gift' has other uses where you cannot use 'present'. For example, a company might hand out gifts to its clients, a magazine might offer a gift to its readers, or a rich person might give a painting to an art gallery as a gift. These are not personal offerings, so they are gifts rather than presents. We also use the word 'gift' for a special innate talent that someone might have, for example, "He has a gift for music".