The most common errors I saw in the first day of stories about the Supreme Court’s same-sex marriage decisions were these:

1. Outlets saying that the Defense of Marriage Act had been struck down
2. Outlets saying (or implying) that gay marriage was now legal in California

Reporting about Supreme Court opinions is always tricky, of course. If you’re not a lawyer or familiar with reading opinions, they can be difficult to understand. There is pressure to be first with the news and tweet it out before anyone else does. And because of that pressure, there is a temptation to write or report the news without first really understanding what an opinion said.

Happily, thanks to the Web, many of these types of errors are caught and changed. For example, if you Google “supreme court same-sex marriage,” you can see that excellent New York Times reporter Adam Liptak originally wrote, “The court ruled unconstitutional a 1996 law denying federal benefits to legally married same-sex couples….” The current version is the accurate one: “In a pair of major victories for the gay rights movement, the Supreme Court on Wednesday ruled that married same-sex couples were entitled to federal benefits …”

Did you catch the difference? The Supreme Court did not, in fact, say that DOMA was unconstitutional. The court only said that the section at issue—Section 3—was unconstitutional. This was the section that said that the federal government couldn’t recognize legal gay marriages performed by any state. Section 2, which says that states don’t have to recognize other states’ legal same-sex marriages, still stands.

I’m sure this sounds like nitpicking until you realize that the difference for actual people is a big one. If DOMA was struck down completely, it would mean that if a couple got married in New York but lived in North Carolina, then North Carolina and the federal government would recognize their marriage. For all intents and purposes, gay marriages would be recognized everywhere in the country. The gay marriage battles would be all but over.

That’s what happened with the anti-miscegenation laws—there was no DOMA-like Section 2. So the fact that South Carolina kept its anti-miscegenation law on the books until 1998, and Alabama keep its law around until 2000, didn’t make a practical difference. Couples in mixed-race marriages could get married in a state where it was legal to do so and then come back home; because of the Full Faith and Credit Clause of the Constitution, a state usually has to recognize marriages performed in other states, even if they don’t fully conform to its own state laws.

But gay marriage does have DOMA Section 2. Which was not struck down. That means that if a couple got married in New York but lived in or moved to North Carolina, then North Carolina would treat them as legal strangers. Whether the federal government recognized their marriage would depend on which agency we’re talking about: the IRS and Social Security Administration base their definition of marriage on where a couple resides, not where they received their marriage license (that is, if a marriage is illegal in North Carolina, then that couple can’t file taxes jointly); the Department of Defense and Homeland Security base theirs on where a couple received their license (which means if you marry in New York and move to North Carolina you can still sponsor your foreign-born spouse for a green card).

In short: When the court struck down DOMA section 3, it meant that married couples who lived in a state where marriage is legal received full federal rights. Otherwise, it’s complicated. Since gay marriage isn’t legal in 38 states (37 when it is fully legal, again, in California), the decision didn’t affect the majority of the country.

Now, on to Prop 8, the ballot initiative that took away the right of gays and lesbians to marry in California. Many headlines were a variation on this one from Talking Points Memo: “SCOTUS Prop 8 Ruling Legalizes Gay Marriage in California.”

That’s not quite right—the headline makes it sound as if the Supreme Court ruled and then people could go ahead and get married. It would be more accurate to say that the ruling “cleared the way for the restoration of gay marriage in California.”

This ruling was especially tricky, because it was so technical. Basically, the court said that, since the government decided not to appeal the court of appeals’s decision, the case should not have continued on to the Ninth Circuit. A private group had no right to come in and argue the anti-marriage case.

Jennifer Vanasco is a is a news editor at WNYC and the former editor in chief of MTV Network's LGBT news site 365gay.com. She writes about social minorities, national politics, and culture. Her award-winning newspaper column on gay and women's issues ran for 15 years.