For full faith and credit purposes outside of New Jersey, it very well might matter if they called it marriage.
That can't be true. We have been assured repeatedly by homosexual activists that a defense of marriage amendment is unecessary because what happens in one state does not affect the others. They will cross their hearts and promise that the full faith and credit provision of the Constitution does not apply. They wouldn't lie, would they?
(Of course, you are right: what these arrangements are called may matter outside New Jersey. If one state recognizes "gay marriage," the other states might be forced to do so under Article IV, Section 1 of the Constitution. Within that state, however, the name is relatively unimportant.)