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A civil union is the joining of two people. It is not marriage and, depending on where you are, it may or may not involve the same rights and benefits that marriage brings. To give two examples, in the UK it does, in the US it doesn't.
 Not equal
So, if, in some countries the rights and entitlements are the same, why have separate ceremonies? Mostly this is to get past those with strong religious objections and who insist that marriage can only be between a man and a woman. This has obvious echoes with the way African-Americans were "separate but equal" in the Jim Crow South. They say a civil union is just as good, though you don't see them lining up to have one.
Politically this may be all that is achievable at the present time. Polls often show more support for civil ceremonies than same sex marriage and, as two New York Republicans are finding in 2012, supporting same sex marriage may be electoral death.
With a key portion of the Defense of Marriage Act having been struck down by the US Supreme Court, the door has been opened for advocates to argue that civil unions are not equal to same-sex marriages, as they do not provide the federal benefits that marriage now does.
On the other side, there are some in the UK who support allowing heterosexual couples to get a civil union, on the basis that it provides a secular alternative to marriage, an institution loaded with historical cultural and religious baggage. This was rejected in the government's recent review of civil partnerships. So the UK situation now is that gay couples can get a civil partnership or a marriage or convert their existing civil partnership into a marriage, whilst straight couples only have the option of marriage. In at least some parts of the US, civil unions are open to heterosexual couples, though few opt for them.
However, even with all these differences, there are some groups of people who won't even tolerate civil unions, generally believing that anyone who performs what they call sexual immorality deserves no rights. Tellingly, many of the people now insisting on this "compromise" fell into the "no rights at all" category before it started to become obvious they their side was losing and it was just making them look like bigots. A rather comical, yet sad event that happened in Texas in 2005 was when lawmakers tried to ban anything "identicle to or similar to marriage" [sic]. This technically banned marriage for everyone.
Civil unions aren't necessarily a bad idea when they're not being used as an excuse to deny gay people rights. If couples want to make sure they're making the right decision before
ruining their lives getting married, a "medium" level of legally recognized commitment might be useful.
 Civil marriage
There is a concept in some states and more importantly, nations outside of the grip of the Religious Right that emphasize the legal sense of marriage by establishing "civil marriages" in lieu of or in addition to religious marriages. These should not be confused with civil unions which are an attempt by the less extreme of the religious bigots to "at least give the gays something."
- 8 Important Distinctions Between Marriages and Civil Unions by undohate.com, video at YouTube