Both are used to express a change in something to fit new conditions. However, adapt is generally more permanent and takes time to achieve, whereas adjust is quicker and less permanent. An adjustment has tends to be more minor, whereas an adaptation is more major. You adjust things to make yourself more comfortable, like a tie, belt, glasses, seat, etc. You adapt to a new climate, environment or lifestyle. I hope this helps.

The verb “adapt” means to change and make suitable for a different use or for new conditions: to adapt a book for children; the eye adapts to dark/light; to adapt to a new situation; to adapt to a new climate The verb “adjust” means to make suitable or convenient for use; to change so as to match or fit; cause to correspond. “Adjust” refers more to the mechanism, “adapt” to the result – We adjust an opera glass in order to adapt it to different eyes. We can adjust machinery; adjust one’s mind to an idea; adjust spectacles, etc.