They're independent of each other. You have to pay for a domain name, I'm not sure where, whereas copyrights you just get by putting your name on your work (it helps to put (c) name 20xx at the bottom, too). You can, on the other hand, trademark your domain name (the .com/.net/.org/etc included or not) at a copyright office (I guess they're technically called patent offices, but we're not talking about patents. Someone pointed out mailing your work to yourself and not opening it to get the date stamp. You can do it more officially and admittedly more expensively at these places). The thing about domain names is once you secure it, it is not illegal, but impossible for someone else to take it.

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Don't frown at your feet,
And give in to strife.
Hold your head high,
It's a wonderful life.