Here we use veterinary in two ways:
1) as the study, and medicine, of domestic animals
2) the place where a veterinarian works, but in this case we always tack on the word hospital (veterinary hospital).

I almost always hear veterinary used as in veterinary medicine or veterinary hospital. If I were to refer to either the place or the person I would use veterinarian.

We say 'take the cats to the veterinarian,' whether we mean Dr Wendy or Cary Animal Clinic

Veterinary=adj. Veterinarian=noun?