Conventional medicine is basically those things done at regular doctors offices and hospitals. Medications, surgery and vaccines are examples. Conventional medicine is taught at Universities and teaching hospital.
Alternative medicine is “any of various systems of healing or treating disease (as chiropractic, homeopathy, or faith healing) not included in the traditional medical curricula of the United States and Britain” (merriam-webster.com)
Veterinarians seek training in alternative medicine after graduating from veterinary school. In the past, alternative medicine was scorned, but now, driven mostly by public request, some modalities, like acupuncture, are being offered in hospitals.
Other names for alternative medicine are complementary, holistic or integrative medicine.
By combining those methods taught at veterinary schools, with methods learned after graduation, the doctors pick and chose between the best of both worlds for the benefit of each individual case.