I would first ask "why" you are taking the dog from the vet, and that will help you to determine how to classify the intake. If you are a municipal shelter, or you are contracted to take in stray animals, then you are accepting the dog as a "stray", similar to the way you would classify a dog that was abandoned outside your front door.
If, however, you are a rescue or a limited admission shelter, and you are taking the dog in as a favor to the vet clinic, I would categorize that as a "transfer". It doesn't really fit as an owner surrender, because the owner did not specifically transfer ownership of the dog to your facility. Hope that helps!
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