Zoology is the study of animals
Veterinary is more medical. They have to know anatomy and how to treat animals for specific things, and I'd think that it probably focuses more on domestic animals, unless you're an exotic animal vet. But even so, it's much more narrow of a study, and then a lot of medical stuff. That's what it seems like to me. In zoology, you're studying all extant species of animals, and can focus on certain types of animals. You could do ornithology (birds), ichthyology (fish), entomology (insects), herpetology (amphibians), mammalogy, etc. It's not really management of a zoo, although you could work at a zoo with a zoology degree.