I think we've finally come to a decision that will work fine for us. I would hate for the other little boy to feel slighted if we didn't get him something. I mean, what if more kids come from Twin A's class and only get a gift for him. Then Twin B would probably not feel very good walking away from that party. And at this age (kindergarten), I think those feelings are normal. Both of them have a lifetime to work through these things.
We will be purchasing gift cards in equal amounts for both boys. This way, they can decide for themselves what they want. I know my kids are always thrilled to pieces to get gift cards. They love picking out their own "stuff" and paying for it themselves.
I never realized this could be such a controversial topic.

It is something we have never dealt with before since my kids have not known any twins up until this point. I totally understand why the parent sent the invite with both names. I'm sure it was just easier for her since it looks as though she ordered customized invitations. It wasn't as simple as writing the names in to the blank ones you buy from the drugstore. No harm, no foul. I'm just super excited that DS finally wants to do a birthday party. He usually avoids them because he doesn't like the noise and interaction (HF autistic).