I saw someone saying that if you send for the record most places will send you the marriage license and certificate together, which might account for part of the confusion about terminology. They're calling it the license because the top piece of paper says that. However if the two get separated, it's the second piece of paper you actually need.

That and a lot of people don't know or have forgotten the difference. For them License=ID. You have the ID that's car-related and the ID that's marriage-related, and they call them both "licenses."