Marriages are a civil union
Should same-sex unions be formed as marriages or as civil unions. Guess what? Marriages are a civil union
Marriage is a civil union
Side Score: 3
Marriage: religious institutio
Side Score: 1
Marriage is a civil union. Lets work this backwards. Is marriage a union? Why, yes. In fact, one of the definitions of union is marriage. 
What then is the definition of "civil"? One definition is "not religious: performed by a state official such as a registrar rather than a member of the clergy" 
Wait a moment. Am I claiming that marriage is not religious? Well, let me ask you this. Where do you go to get a marriage license? To your local Hari Krisna Temple? And where do you go to get divorced? To the Scientology Center where they do away with your "until death do us part" vow before God and absolve you of going against the command "What God has joined together let no man put asunder"? No, you go before a judge.
Some people choose to have a marriage ceremony in a religious institution. But it is not necessary. Neither is it sufficient. You are not legally married without a license from the government.
In fact, well before religious institutions performed marriage ceremonies, "traditional marriage" was a "common law" marriage. After people lived together long enough, they had the legal status of a married couple. It was religion that moved in on what before was a purely civic matter.
In the debate about same-sex marriage, some folks say, "Let them form civil unions instead and leave marriage to the religious." Um, no. Some marriage ceremonies are religious. But all marriages are civil unions. If some religious institution wishes to allow same-sex marriage ceremonies, that is up to them. However, it is up to the government to give same-sex couples the right to marry.
Remember. Same-sex couple want equal rights, not equal rites.
Side: Marriage is a civil union
I'm going to add the argument to this side although in all honesty, the answer is "both".
The history one prescribes to will have a large effect on what one thinks is the origin of marriage. Those of the Judeo-Christian line of thinking will say that marriage started as a religious institution with the creation of Adam and Eve.
On the other side, marriage has been used in so many ways by so many cultures that it's origins are truly muddied. Regardless, it has been used by both civil and religious institutions over several centuries.
I can go into a church and have the minister marry me and my spouse without ever having to go through a court or legal proceeding. My marriage would be recognized by the "church" but not by Gov't. Likewise, I can have my marriage recorded by the state, but there is no law that requires the "church" to reconize that marriage. In this day and age, and in most countries the two have become synonymous. However, they are truly not the same as the beginning of the paragraph shows. It is like saying that a Pembroke Welsh Corgi and a Cardigan Welsh Corgi are the same. They are very similar, almost identical, but they are not the same.
In the end, a civil marriage is one created by the rules of a government and a religious marriage is one created by the rules of a religious institution. Just because some or even most of the rules are the same, not all of them are and thus they are not the same.
Side: Marriage: religious institutio