If you are interested in the laws of nature, such as quantum mechanics, Einstein's theory of relativity, the Grand Unified Theory, string theory, loop quantum gravity, and so on, you should study physics.
If you are interested in stars, planets, the moon, the sun, the solar system, how galaxies were formed and evolve, you should study astronomy.
There are also areas that are pursued by both physicists and astronomers such as cosmology and astrophysics. Cosmology concerns the evolution of the universe in a large scale, and many prominent cosmologists, such as Alan Guth who first proposed inflation, have been theoretical particle physicists.
I have a couple of friends who studied physics as an undergraduate, then studied astronomy as a graduate student, and became astronomer. You may consider this option if you are not sure whether you want to study physics or astronomy because it is much harder than the other way around. (studying astronomy as an undergraduate student and then studying physics as a graduate student)