A truly useful approach to animal behavior and veterinary science integrates the two at every step—history taking, physical exam, diagnostic plan, treatment, and follow-up. The question should never be "Is it medical or behavioral?" but rather "How are they influencing each other?"
Historically, our understanding of animals was often shaped by folklore and "just-so stories". In the Victorian era, natural history texts were popular but highly anthropomorphic, often attributing complex human-like motivations to animals.