The science of astronomy and the ancient science of astrology actually do have a lot of parallels to them. While the modern tabloids have turned astrology into little more than a series of extremely generic predictions designed to get some money out of the pockets of people who do not know any better, its ancient practice was based on the positions of the stars, planets, Sun and Moon in the heavens. People really did believe that the sign under which you were born (and also the signs that were most overt at any given moment) were very important to identifying who you are, what you need to do in your life and even what your future would hold. By contrast, astronomy is a very modern identification of where and what the various objects in space are, coupled with (the best guesses about) how they got to be that way in the first place.
Some people would say that the lack of a formal science in astrology, and its reliance on the very right brained interpretations that some people are capable of providing (or simply making up through quality cold reading) make it very different than any kind of a science could be. After all, while scientists do base their judgments on their observations, they generally refrain from making such bold and far reaching statements as to imply that they have the power to tell the future through what they observe in the natural world. Astrology, on the other hand, has no such inhibitiions about what they are willing to say.
The funny part about it is, in the classical sense, astrology has actually been a genuine science. Since it was based on the observations of people who took the time to study where the various stellar bodies were at any given time, there was a very deep vein of fact behind it. While this vein of fact has been largely obscured through the existence of various types of scams and ridiculousness, it does stand true that the most major deviation between astrology and pure science has been through modern silliness.