For two words so similar, they could hardly be more different in meaning. Astronomy is the study of celestial objects; in short, objects outside the Earth’s atmosphere. Astrology is a philosophy that teaches that placement of celestial objects – the sun, moon and stars determines and influences your personality. Astronomy is a science whereas Astrology is is a pseudoscience. Historically, the two disciplines were related but parted ways in the 17th century when core scientific principles such as the Earth revolves around the Sun which is the centre of the solar system became widely accepted as fact.
Put in another way; Astronomy is the study of celestial objects and Astrology is the study of how the position of said celestial objects affects mood, personality and world events. Astrology is not empirically provable. There is no evidence that the predictions made by Astrology are true and many followers of Astrology suffer from Confirmation Bias – that is, they tend to believe outcomes that support their preconceptions: cherry picking the evidence as it were. Simply put, they believe that Astrology is true and confirm their belief by only paying attention to the data that supports their belief and ignoring evidence against.
Astronomy’s divergence as a separate science began in earnest with the invention of the telescope. Until then; ancient civilizations studied the predictable movement of the sun and stars and used this data for celestial navigation and calender making. The science of Astronomy as we know it today could also be called Astrophysics.