Correct term for having lost (not cut) one's hair

You are quite correct that simply describing someone simply as bald is ambiguous: it could mean that they can no longer grow hair, or that they have cut off all their hair.

To disambiguate:

Gone bald describes someone who has lost the ability to grow hair.

(Closely related, balding or going bald describes someone who is in the process of losing their ability to grow hair; either their hair is thinly distributed, or they have a (presumably small, but definitely increasing in size) bald patch.)

Shaved describes someone who has cut off their hair. (You'll generally want to specify what part of them has been shaved; saying "John has shaved" is not the same as saying "John has shaved his head".)

A reputable medical website http://webmd.com describes the condition alopecia as the medical term for baldness.

Notwithstanding a variety of treatments, cosmetics and quackery, the condition is more or less permanent.

Hairless, on the other hand, could be the result of a mechanical, not a bioogical process, and can usually be remedied by time and follicular activity.

Honestly, I think that "hairless" is also too ambiguous. It could mean that it never had hair to begin with.

I'd go with "gone bald." If you just say "bald" it could be temporary, but "gone bald" has a strong implication that it's more or less permanent.

"Hairless" is also ambiguous because it does not refer specifically to head hair. It could refer to a chest that appears hairless, and that would be a more common usage.

A more obscure word meaning the same as hairless is glabrous.

glabrous gla·brous (glā'brəs) adj. Having no hairs or projections, especially on body parts that normally have hair; smooth.

If the person in question still has some hair, you could go with balding, which strongly implies a natural decline in hair, as with age.