While there is room to argue your point, not only do I think it is meaningless, but I think it’s actually potentially harmful to the movement to make a distinction and, as you seem to be in favor of it, I would imagine you’d see it as a bad thing.
First, I think it’s a meaningless distinction for reasons others have covered above. Sure, gays can marry, so gays being able to marry isn’t the issue. One could also easily interpret it to mean a marrige in which the gayness (for lack of a better term) is a defining characteristic; that is, a man marrying a man is undeniably a gay marriage, while a man marrying a woman, even if one or both is actually gay, is in line with a traditional marriage and therefore not necessarily gay; That is, the first is a type of marraige in which a gay individual may be interested, while the second probably isn’t, and I don’t think it is misleading to call the first type of marriage a gay marriage. Further, the term gay marriage it is already understood by most people to refer to men marrying men and women marrying women; I imagine that for most people, that would consider the terms gay marriage and same-sex marriage to be synonyms.
More over, same-sex marriage is a longer and less direct way of saying it. If I see two guys holding hands, I don’t think of them as a same-sex couple, I think of them as a gay couple or a homosexual couple, or other similar terms. That is, I’d think that using the term same-sex, if it does anything, is actually more distant than gay because calling it gay marriage helps drive home to someone who identifies as gay that it is a problem that is relevant to them. And, while this isn’t my personal perspective, I could even imagine to those who oppose it for ickiness, the term same-sex probably drives home the ickiness more because it emphasizes the sex part of the relationship while there’s plenty more to a marriage than sexuality.
That said, I have even heard arguments very similar to the one you’ve made being used in opposition. That is essentially that banning gay marriage isn’t discriminatory because gays can get married now, just like everyone else.
But really, if you are in favor of legalizing it, this is just a big fat waste of time. Make your arguments about women’s suffrage and interracial marriage (the latter of which I think is a particularly relevant historical analogy), but arguing over the term (unless it were something offensive or counter-productive like “fag marriage”) is just adding noise, which dilutes the saliency of the points being put forth by its proponents. And really, it doesn’t even matter, because no matter what you call it, it’s still icky to people who think it’s icky, it’s still a sin to many to those who believe in legislating morality, and it will still destroy the family unit to those who believe that.
