If you get a dog from the shelter they will be up to date on shots and fixed. You would only have to register them. If you rescue one from say just a random person you'll have to get the rabies shot and will have to have them fixed. But if you adopt from a licensed rescue they will also be fixed but not all keep up with the shots.
When you adopt a dog you are giving it a permanent home. Rescuing a dog might mean the same thing, but it might also mean providing "foster care" for that dog, a temporary home while a permanent home is found.
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