Though the practices of astrology and astronomy have common roots, there is an important distinction in astrology vs astronomy today. Astronomy is the study of the universe and its contents outside of Earth’s atmosphere. Astronomers examine the positions, motions, and properties of celestial objects. Astrology attempts to study how those positions, motions, and properties affect people and events on Earth. For several millennia, the desire to improve astrological predictions was one of the main motivations for astronomical observations and theories.
Astrology continued to be part of mainstream science until the late 1600s, when Isaac Newton demonstrated some of the physical processes by which celestial bodies affect each other. Since then, astronomy has evolved into a completely separate field, where predictions about celestial phenomena are made and tested using the scientific method.
In contrast, astrology is now regarded as a pastime and a pseudoscience—though thousands of people around the world still invoke advice from astrologers and astrology publications in making important professional, medical, and personal experiences. (This, despite the fact that current horoscopes rely on outdated information!) Yet there's a reason people continue to rely on horoscopes: read the Focal Point column in Sky & Telescope's August 2015 issue to see why astrology "works".