Horary astrology is an ancient system used as a divinatory tool to answer specific questions asked at a specific moment in time. A chart is then erected for the time, date and place of the question itself. That chart is then read by very specific rules, and an answer to the question can be ascertained. It is used most often for finding lost objects, along with many other types of questions. For more information, I strongly recommend Anthony Louis' Horary Astrology: The History and Practice of Astro-Divination, Llewellyn Publications, 1991. It's thorough, well-written, and highly amusing besides.
Vocational astrology is a subspecialty that focuses on helping a client find career direction and fulfillment using the natal chart as a guide. It focuses particularly on the 10th, 6th and 2nd houses, as well as their rulers and residing planets, while taking the personality of the individual into account as shown by the natal chart as a whole..
Medical astrology is a subspecialty focusing on the chart as an indicator of health strengths and weaknesses. It is, of course, very dangerous to consult only your chart and diagnose yourself without proper medical diagnostics and treatment. That being said, medical astrology can be a valuable tool in assisting you in understanding what body system weaknesses you may possess, thus allowing you to alter your lifestyle to promote a healthier, longer life.
Business and financial astrology is yet another subspecialty, focusing on financial arenas, such as the stock market or personal finance. Business astrology uses the chart of the start of the business as a natal chart.
Relocational or locational astrology is place-centered astrology. Some astrologers read the natal chart adjusted for your current location, as the location changes your natal chart to some degree. For instance, if you were born in LA and move to New York, a chart cast as though you were born in New York will shift your chart and may more accurately reflect what your life is like as a New Yorker rather than a person from LA. You may have been born with your Venus in your third house in LA, but it falls on your Ascendant in New York. Thus, New York may be a better place for you to look good or meet a love interest than LA was. There is a particular form of this type of astrology invented by Jim Lewis called Astro*Cartography (TM). It creates a map of the entire planet, showing where your planets will fall on the angles anywhere on earth.
And this is just the beginning.
Enjoy your exploration of astrology in all its many facets, and may the stars shine brightly upon you!