What exactly do same-sex couples want

Maybe I have not followed the issue closely enough but given the proliferation of posts regarding same-sex marriage rights, perhaps someone can articulate exactly what is meant by this.

My understanding was that most if not all developed nations, including the US, had allowed civil union marriages for more than a decade and same-sex couples in de-facto relationships had the same rights in law as any de-facto couple.

So is this or is this not the case? From any research I have done it seems to be the case, but perhaps I have not been thorough enough. If it is not the case then I can understand but if it is the case, and from what I can see it is, then what is the issue about? What do same-sex couples want? Is it the right to be married in a church, mosque, synagogue or temple?  If it is then they are probably pushing for something which has as much chance of happening as all sporting codes being required to admit either sex as players.

And while one may disagree with much about religion, and I do, surely they have a right to decide what their beliefs are and people may choose whether or not to become a member of that religion. In reality, no-one has the freedom to choose to be married in any religion unless they fit certain criteria.

I would love to see a clear articulation of exactly what it is same-sex couples want as opposed to 'fluffy' posts and images presenting it as a human right.

Personally, if religions can be forced to change their teachings to force same-sex marriage through, I would have thought a more important issue to be forced through was gender equality!