Tags and registration are generally considered two separate things:
Tags are used just for identification. They usually include the owner's phone number and/or address, so that if the dog runs away and is found by a stranger, that person can call the owner to retrieve the dog. Tags are much quicker than other forms of identification, such as microchips, because the person finding the dog can immediately call the owner. These tags are optional, unless your local laws say otherwise; personally I don't have tags on my dogs because the jingling drives me crazy.
There are also rabies tags, which you get from your vet whenever you get a rabies vaccination. Rabies tags are a quick way of showing that your dog has his rabies vaccination, in case the dog bites a person or other animal, or in case the rabies status becomes a question. You can put these on the dog's collar as soon as the vet gives them to you.
Registration is a local law. Most cities or counties have laws about registering your dog, and they all have different rules about how they prove registration. I suppose some probably have tags you receive after registering your dog, similar to the rabies tag. My county does not require registration, so I don't really know how it all works.
I'm not sure if I answered all of your questions, let us know if you need more information!