Hmmm... Aside from the wording then, what's the point of calling a civil "marriage" something else? In the US at least, there is zero concordance between a church marriage and a civil one.
Two people can walk up to a Justice of the Peace, witnesses in tow, sign some paperwork (and pay an administrative fee), and be civily married. That gives them the legal status of being married, which includes a number of purely secular benefits including including joint guardianship of eachother and any children they produce, automatic power of attorney over eachother (and children), and automatic inheritance from eachother (and to any children).
There is nothing religious involved there. Nothing at all.
Two people may also choose to get a religious marriage. The process varies, but generally requires a priest to perform a ceremony. This grants them the status of marriage within the church, which basically just absolves them from sin when they have sex together (and may or may not last into the afterlife, or even into future reincarnations...). Oh. And children produced by them aren't going to be bastards in the eyes of the church.
See! Two completely different things, yet also somewhat similar. A church wedding does not conver the civil status of marriage, and vice-versa. One is not required for the other to take place (although most churches will require a civil marriage take place before they'll grant one in the church, and many priests that perform wedding ceremonies are also bonded with the state to allow them to conduct the civil ceremony as well).
I had a friend of mine perform the wedding ceremony for his brother. Since it's a purely ceremonial service, anyone can do it. However, they still had to do the civil stuff and fill out the paperwork to be "legally" married.
So I guess I don't understand why it matters what we call it. I suppose we could rename the civil marriage to "civil union", but in my opinion, that's just as silly as legistlatively renaming "Evolution" to "Biological changes over time". It's still the same thing, and the reasons for changing the name are equally invalid. Just because a religion has a ceremony with the same name as a state status does not mean that two are the same. Civil marriage convers some very "legal" things that have nothing to do with religion. Religions do not collect income taxes in the US. They do not establish inheritance. They do not grant power of attorney. They do not grant guardianship. They don't do any of those thigs in the US. The government does. Thus, it is completely appropriate for the government to perform and regulate the status of "married" as it applies to those purely civil issues.