With an annulment, the Catholic Church examines a the original marriage contract to see if it was entered into and executed validly, that is, the Church examines to see if there was ever a marriage at all. If it is discovered that there were impediments to the marriage, then a valid marriage was not entered into and so was not preformed. Therefore the two parties are single, and have always been so (unless one of them was in a previous marriage to the one examined, which is itself an impediment).
A divorce does not examine the validly of a marriage. Whether it is valid or not, the state simply declares it void. Divorces are not recognized by the Catholic Church.