A divorce is a legal term ending a valid marriage.
An annulment declares that a valid marriage never existed.
People tend to think of annulments as strictly a church thing but annulments can be a legal thing too. Usually people who might have grounds for a ‘civil’ annulment opt to get divorced instead because proving those grounds takes a lot longer than simply getting a divorce.
Well, kind of. A divorce decree states that a marriage is dissolved, but, as you point out, the matter of whether or not the marriage was valid in the first place need not be fully investigated.
A decree of nullity exists in both canon law and civil law. It means that the marriage has been declared to have never legally existed. For instance, a couple who can prove that one or both parties were underage, incapacitated by alcohol or drugs, or that one or both parties were already married to someone else at the time vows were exchanged can obtain decrees of nullity from both the Church and the state. The required elements for a valid marriage differ from canon law and between various jurisdictions of civil law, though. For instance, as I understand it, a Catholic who married an unbaptized person without dispensation from the Church and without leaving the Church might receive a decree of nullity from the Church for that marriage, but would usually find that the state would not find the marriage null, since most governments do not require that dispensation as an element of a valid marriage between a Catholic and a non-baptized person. (I don’t know of a single government that does, but one could exist.)
An annulled “marriage” was not a marriage, but rather an attempt at marriage. Unless there was fraud, it is presumed the attempt was made in good faith. A decree of nullity doesn’t turn the clock back, it doesn’t mean that the couple’s children are “illegitimate”, that consumation of the attempted marriage was fornication, or anything like that. It just means that for purposes of future actions, the marriage is treated as though it was never contracted.
Also, many people do not know that the Church will not investigate a marriage for a decree of nullity unless the marriage has been dissolved in civil court by divorce or annulment first. This is so that the Church can be assured that the process of investigation will not alienate the affections of a validly married couple that might have had a chance at reconciliation. As far as the Church is concerned, marriages are presumed valid until shown to be invalid.
Also, if a marriage is declared null by the Church because of psychological
incapacity of one or both parties, that can be an issue with regards to whether the incapable party will be considered
able to marry down the road. The null marriage does exist as evidence concerning a person’s ability to contract a valid marriage, too, then. A decree of nullity from the Church isn’t necessarily carte blanche to attempt marriage again.
That is my understanding of it, though.