Veterinary school is 4 years in length. Internship or residency credits are not required but may be offered to achieve advanced qualification or specialty certification.
There is a national veterinary medical board exam that you must pass after completing vet school. Ohio does not have a state board exam, but some states require one in addition to the national licensing exam. Each state has their own requirements and some states have reciprocal agreements, meaning that if you pass the state board exam you are eligible to practice in another state.