Not always. A present usually refers to a tangible item that you give someone. A gift includes a more wide variety of things. For example, gifts can include money or other intangible things such as "the gift of life". You would never say the "present of life". So to sum up, you could say "gift" or "present" for most tangible things, but for some things, only "gift" would be appropriate.

I would say in general they are interchangeable. I have not been able to think of an exception yet, I probably will after I write this. Haha..