Comment: They're not

To the best of my knowledge - background check is exactly that. It doesn't confirm that you have purchased a firearm. You can be checked and then come back and say - "nah, don't want the firearm"...

As for CCW - it's also not a firearm registration. All it does is it certifies to the state that you can handle a firearm and so you're OK with carrying it loaded outside of your home.

I know that in theory both are potentially infringing on the right to bear arms, but I think it's the battle that most gun owners (and gun lobbies) are willing to ignore for the sake of focusing on more important issues like gun registrations, gun bans, etc.