Hello,
That is a very good question.
There is a small difference in the pronunciation.
Adapt sounds like A-daapt, where the 'apt' part sounds like the word app
Adept is pronounced shorter than Adapt is. So it sounds like A- dept, where the 'dept' part sounds like 'depth' without the TH sound at the end, just the T.
So in short, adapt sounds longer on the A, where adept is very short on the E.
Pascale!