Marriage is one of the seven sacraments, which are outward signs of God's grace. Marriages are instituted by the church. A civil union is a contract between two people. Civil unions are instituted by the government. That's the easiest way to tell the difference between the two, although it's a bit harder to see this in a place like Britain, where the government runs the church.
Brace yourselves. I'm about to show a picture from a 1949 catechism.

(click on the picture to see a larger version)
In #1, we see a Catholic wedding between Joseph Goodman and his wife, Mary. Joseph and Mary are both fully initiated Catholics. They have, of course, undergone seven months of marriage preparation. (Note that this is marriage preparation, not wedding preparation. Some people mistakenly think the wedding ceremony is more impotant than the marriage.) Their marriage is celebrated during a mass, inside a church, before a validly ordained minister and at least two witnesses. Jesus and the angels smile upon their wedding.
In #2, we see Paul Agan contracting a civil union before a Justice of the Peace. Maybe he thinks marriage is just a piece of paper with the words "Mr. and Mrs. P. Agan" on it. Maybe he hasn't been to church in years, because it cuts in on his football-watching time. Maybe he doesn't care about marriages at all, and he's being forced into it. Whatever the reason, he isn't getting married in a church, before a validly ordained minister. Instead, he's letting the United States Government do the job. Note that Paul's guardian angel hides her face in shame, and Jesus is decidedly looking the other way.
In the eyes of the Catholic Church, marriage must be performed in front of a validly ordained minister and two witnesses. That's a general standard, obviously. There are more requirements, such as "neither the bride or the groom can be married to somebody else", but I won't go into them here.
According to these standards, most civil unions (or "government-appointed marriages", whichever term you prefer) are invalid, at least in the eyes of the church. A good deal of marriages performed in non-Catholic churches don't count as valid, either.
People may question the Catholic Church's stance on government-appointed marriages, but let us remember that here in the United States, the church and state are separate. The government, therefore, does not have the right to exert religious authority, especially in matters like marriage. This is why a government-approved marriage is called a "civil union", not a marriage. The authority the government exerts is merely civil authority, not a religious one.
One final word on the government and marriage. Catholics should obey the state's laws on marriage, as long as these laws do not contradict the laws of God or the church. There are some state laws which do contradict the laws of the church, such as the laws on civil divorce. Citizens are recommended to work to get these laws changed, so our legal system may be more just.




