What is the difference between "unbeliever" and "disbeliever"?

I am asking this question because of this question from Islam.SE.

It seems that "unbeliever" can be used for a person "who does not believe" whereas "disbeliever" can be used for a person "who is presented and rejected". The prefix "dis" can be used for rejection (compared to the prefix "un" which can be used for "not" without rejection). So "disbelieve" seems to imply "making a conscious decision" to reject/dismiss something.

How correct is above explanation. Can someone explain in more detail what is, if any, the difference between those two words?

That seems a reasonable definition. Unbeliever or non-believer is someone who is outside the faith, either by choice or because they haven't been told. Disbeliever implies a deliberate and definite rejection of the belief.

This would be a reasonable definition in a scientific or generalised philosophical context, but unfortunately religion, where shades of meaning can be vital enough to cause wars, has developed specialised terms. A non-believer is simply somebody who does not share the faith under discussion. An unbeliever, as I understand it, is somebody who has had the chance to believe, but rejected it. An infidel is somebody who follows another faith; both these last two are disparaging, at best. ?Disbeliever is not in common use, because so much would depend on exactly what has been rejected. Rejecting a tradition peripheral to the religion might make you a reformer, unusual but orthodox or perhaps a member of a different sect or denomination; rejecting important dogma might make you a heretic (somebody calling himself a [Muslim, here] but actually not), and it is not objectively clear (at least in a linguistic context) which is which.

I consider myself a non-believer. In this I simply do not have a belief in whatever the object under consideration may be. In religious terms, I am an nonbeliever in God.

I consider this different from an unbeliever. In my philosophy, and unbeliever is the opposite of a believer. A believer has a positive believe in the existence, truth or validity of the object of belief. An unbeliever has a positive belief in the non-existence, non-truthfulness or invalidity of the object of belief.

I would equate an unbeliever with an atheist. However, in a needless act of splitting hairs, I do not view non-belief as the same as agnosticism. As the believer positively believes in the existence of, the athiest positively believes in the non-existence of, the agnostic postively believes in the inability know one way or the other. The non-believer just does not care and has no belief one way or the other.

Existentially, the existence or non-existence of the non-believed in object is irrelevant for the non-believer and does not matter, whether or true or false. The non-believer may find the arguments for or against belief interesting and even intellectually compelling, but inevitably these arguments are simply an exercise in analytical thinking and metaphysical inquiry. They aren't, however relevant, and so do not factor into subsequent decision making.

Believers and unbelievers will deliberately construct other elements of their philosophy and life's vocation from the belief they hold. For non-believers this is not necessary.