Astronomy and Astrophysics is the study of planets, stars, galaxies, and the Universe as a whole. This includes how all of these originate and their evolution in time. The principal pursuits of an astronomer are to extend our understanding of the physical nature of the Universe and to convey this understanding to colleagues, students, and the general public.
Astronomy is an observational science. With only a few exceptions (meteorites and moon rocks), we cannot actually experiment on or touch celestial objects and are totally dependent upon incoming electromagnetic radiation, light, from space. Observations over the entire light spectrum (gamma-ray, x-ray, ultraviolet, visible, infrared, microwave, and radio light) are collected with both Earth-based telescopes and space observatories. In recent years, multimessenger astronomy is increasingly possible, studying events using light, gravity waves, and particles at the same time. All of these observations are analyzed using the tools of modern computing and statistics. Theoretical astrophysics uses state-of-the-art physics and supercomputers to recreate the physical processes numerically in an attempt to match the observations.
There is no difference in Astronomy or Astrophysics here at Ohio State they mean one and the same. The heart of the prospective astrophysicist's education consists of a firm grounding in physics plus advanced mathematics to understand those physics concepts.