It's simple, Bosun. You adjust other things, not yourself. As Gasman says, you can adjust your approach; or your trousers. You can also say, that someone has adjusted well to his new environment, but that would probably not be as usual as to say he adapted to the environment.
No one is going to shoot you you if you use them interchangeably -- we're trying to show you the subtle differences of common usage.
To be precise, adjust means to change or correct, usually incrementally.
Adapt means increase the degree to which you conform or fit in.