I think this paragraph from the article explains it clearly, eloe. (BTW, how should I pronounce your name?)
"The way to deliver both is a proper separation of civil and religious marriage, so it is clear that civil recognition of relationships is a matter for the state, defined in law, and this should be the same for all couples, but at the same time then allowing belief-based organisations to marry whoever they want according to what they believe marriage to mean."
So, in a nutshell, marriage will be a civil partnership, but if anyone wants to add on a religious aspect/ceremony, that's up to them and separate. An addition to the legality, if you like.