What do the LGBT Community want from a "Yes" Vote?

So this is a question that has been bothering me for a bit in relation to the upcoming referendum.
Now I'd be lying if I said I was fully informed in the differences between marriage and a civil union, but I'll give this a go anyway.

So I am really curious and unaware as to what members of the LGBT community want want if a "yes" vote were to occur.

When I think of marriage, I think of a ceremony where a bride walks down the isle of a church, the priest does is job, and then bob's your uncle.

But with a "yes" vote, this will still not be the case, due to the fact that most religious institutions are against homosexual marriage (not something I entirely agree with, but that's a sad fact).

So with regards to the differences between a marriage and a civil union, all tax stuff and similar things are equal, so a "yes" vote will make no difference in that regard.

But the biggest thing I see a difference with comes back to family. Such as a family home and a shared home, and also the legally recognised relationship between a child and there biological parent.
My first question is, shouldn't the definition of a family be changed, as opposed to marriage?

And secondly, is it just that LGBT members want to be able to ask someone "Will you marry me?", and to tell people that "I'm married"?
Or is there something much more that I'm missing.

Right now I'm on the fence as to which way I'd vote. Although a lot of the "No Campaign" posters seem irrelevant to marriage (focusing on surrogacy and other irrelevant topics), there is one poster that stands out to me, which reads;
"We already have civil partnerships, why redefine marriage?"
To be honest I think that is a fair statement, and I would like to know why marriage needs to be redefined, as opposed to either redefining civil partnerships or the family.