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?