"Aster" or "astro-" means star in Greek.
"Nomen" or "nom-" means name in Latin, and "-onomy" means "the naming of."
"Logos" or "log-" means word in Greek, and "-ology" means "the study of."
So, both of these fields have named themselves as those who study the heavens. Both of them "study" what goes on up there. Astronomy could have named itself astrology, but we need different words to distinguish what are really very different things.
Scientists interpret astrology as bunk - pseudoscience that doesn't stand up to the level of scrutiny that a scientific hypothesis must withstand to be considered possible or right. When horoscopes are wrong, no one stops believing their horoscope, because they don't read it for its reliability - they read it out of psychological need, or curiosity, or even faith. But the beliefs held by astrology are borrowed from the beliefs of philosophers from thousands of years ago about what those funny lights in the sky were, and how they might influence us. They don't admit the reality that they are balls of rock and gas so far away that their gravity doesn't even change our weight on a scale appreciably, let alone whether you will find money or love in the future.
Basically, astronomy studies celestial objects for what they really are. Astronomers gather data on these things, like brightness, distance, mass - real things. Astrology is a kind of mystical fortune-telling that supposes that magical forces are at work in the universe, and that is dying a slow cultural death.