Astronomy is about the study of stars and planets, their behavior, birth, distance, etc. - way to do it is by telescope; on a bigger scale by hubble space telescope. It can be studied in multiple ways. Considered a natural science.
Astrology is about the study of stars affecting a persons life - date and time of birth will be accorded different stars, affecting their lifecycle - different methods of astrology over the years, Chinese, Western and Hindu are the main ones. Considered a pseudo science.
Both subjects have been more of a fascination to me than an actual interest, so the description by me are more layman.. :)