Do they both have universally accepted legal definitions, and what are they? Or do they vary from state to state?
To oversimplify, a divorce says that a valid marriage has now been terminated. An annulment says that the marriage was never valid in the first place.
Catholicism also states a marriage must be annuled by the church to be seen as valid. From what I understand, you have to prove that your marriage should never have been or was taken place under invalid circumstances. When my ex-gf (Catholic) and I (a divorced Protestant) were talking about the possibility of getting married, I found out I’d have to basically make my case to her church for an annulment to be granted so they’d approve the wedding.
An annulment can also occur under state law, and the meaning is essentially the same: the apparent status of marriage between these two people is deemed to have been entered in error (or fraudulently) and the marriage is dissolved.
This would mean, for example, that the (former) spouses could not be held liable for various debts that one or the other acquired. It occurs most frequently when the marriage is challenged because one partner was below the age of consent.
Annulments were also given in cases where it was shown the two parties never consummated their marriage.
Though the terms can be confused. For instance, most people “know” that Henry VIII divorced two of his wives; actually, he had (or tried to have) the marriages annulled, from Catherine of Aragon because it was incestuous, and from Anne of Cleves because it was never consummated.
I have been through both. The annulment was after a 2 month whirlwind romance. One day I took her to a court house that her mother worked at and we walked out with a marriage license. 3 days later the judge her mother worked for married us. 2 weeks later she was offered a job in New York (she worked for a national advertising agency) and the offer was too good to pass up. I had just been rehired by a large commercial aircraft manufacturer 6 months earlier and I had no desire to live in New York. We went back to the judge, he granted an immediate annulment and it was just like the marriage never happened.
Oh, and the marriage was consumated. Many times. 