In addition to what bauer said, they have different connotations. Specific is like "THE bird" instead of "A bird". You're talking about an object in particular instead of in general. i.e. When I say "look at that bird in the tree", I'm not talking about any bird around, I'm talking about the one I'm pointing to in the tree, that specific bird.
Special can also mean nice, or treasured. It is a very kind word (unless you're being sarcastic or in reference to "special education", which is an exception). If I say "the gift you gave is very special to me", it means you gave me a gift that is important to me and one that I like a lot more than most gifts I receive. A special student is one that is high-achieving, etc. But, like I said earlier, special can also have kinder meaning for things that aren't so good, such as when "special education" means a slower learning given to people who have a more difficult time at school for physical or mental reasons.
My point is, you can use "special" as "specific", because it can mean the same thing. But you can't use "specific" to mean "special", because "specific" doesn't give the kinds of feelings that "special" does.