The one they were given said La La Land...
“It begs the question: Why would there even be an envelope that said La La Land?”
Apparently envelope cards are written up for each film. And then the correct card is placed inside the envelope only that night, or right before the announcement. That way no one knows ahead of time except for whoever has a list of the winners.
They were given an envelope that said, "Emma Stone" and underneath it said, "La La Land".
Which means that they were given a duplicate of the Best Actress envelope. They were confused why the Best Picture card inside the envelope would have Stone's name, but interpreted that to mean that La La Land won best picture.
Beatty and Dunaway didn't make the mistake. Whomever gave them the envelope made the mistake.