I am asking this question because of [this question from Islam.SE](https://islam.stackexchange.com/a/2158/44).

> 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?