What's the difference between astronomy and astrology?

Over the last few years I have had a number of conversations, with a wide variety of people, that have included an exchange along the following lines:

"What course did you do at uni, then?"

"Maths with astronomy."

"Astronomy? So, like, you can work out when I'm going to win the lottery, or something?"

"No."

So what is the difference between astronomy and astrology?


Astronomy
Astronomy is the branch of physics that deals with the study of the universe, the things in it, and they way they act and interact. This study is undertaken through scientific investigation- observations, experiments and mathematical inference. Although it is a subset of physics, it also has links to branches of chemistry, geology, biology and other areas of science.
The terms 'astronomy' and 'astrophysics' are almost interchangeable, but astrophysics tends to deal more closely with the movement and physical properties (size, mass, temperature, composition, etc.) of celestial bodies (e.g. stars, planets, asteroids, galaxies, etc.) and is more theoretical, whereas astronomy is usually more observational in nature. Obviously, many advances in any particular field of astronomy are made by a combination of theory and observation, and so it is difficult to include either one as a subdivision of the other.

There are a number of sub-branches of Astronomy, including astrobiology, cosmology and planetary science, which interact with each other in different ways.


Astrology
Astrology is a group of beliefs or traditions that claim to use the relative positions of the planets and other celestial bodies as viewed from Earth to predict future events and occurrences. Put another way, astrologers believe that the motions and interactions of celestial bodies directly influence life on Earth. It is not widely considered to be a scientific discipline.

The core beliefs of astrology are illustrated by the Hermetic principle 'as above, so below,' which sums up the idea that events in the heavens are in some way repeated down on Earth. Past astrologers relied on regular observation of the heavens in order to make their predictions. Today, many astrologers use data collected by astronomers in order to predict (or confirm) the motions of the planets.


You can read through some absolutely non-serious and completely made up* horoscopes here.


Why the mix up?
Astronomy and astrology were essentially one and the same for much of human history, but the two started to diverge during the Renaissance (14th - 17th Centuries ACE). During the 18th Century astronomy established itself as a scientific study whilst astrology continued along a more superstitious route.

To some extent it is easy to see why astronomy and astrology are still mixed up in the minds of many people even today. Both involve some level of study of the stars and planets, and astrology does require a certain use of mathematics to predict the movements of celestial bodies. Therefore, on a very basic level, the two are indeed still linked. Once a deeper interest is taken in either discipline, however, clear differences soon spring up.





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* Many people would argue that all horoscopes are completely made up.