The meaning of adaptation is the act of adapting or the state of having been adapted. That is to say an adaptation is something that is changed from one state of being to become something different yet still similar to the original. For example, an aircraft type that is subsequently altered to cope with different conditions such as having a strengthened airframe can be said to be an adaptation of the original type. Or a movie that has been largely based on a book is an adaptation of the original work.
The differences between adaption and adaptation do not seem to be marked, and this is backed by most dictionaries consulted. For example, the Oxford Advanced Learner's Dictionary simply states that adaption is a less-frequent synonym of adaptation.
A Google search confirms that adaptation (104 million results) has a far more accepted and popular usage than adaption (24 million results). While far from scientific, it does seem to confirm the common view that adaptation is literally the "correct" usage of the word for its meaning. Meanwhile, adaption -- while not strictly "incorrect" -- is less popular and recognized, may lead to confusion, and may even lead to correction in formal business or academic settings.
As has been mentioned, most people will use the term adaptation while a few will use the term adaption. In general, language like this will almost go unnoticed and doesn't strictly matter although to be perfectly clear it would be advisable to use adaptation. Many reputable publications seem to agree with the usage such as "The New York Times" and the "Washington Post."