There are generally two categories:
Yang （阳宅） – For the living
Yin （阴宅）- For the dead, ancestors, burial / tombstone
YANG FENGSHUI （阳宅）
It is not about 8 Mansions （八宅）, Flying Stars （飞星）, 64 Hexagrams, San Yuan （三元） or San He （三合）. These are just formulas.
Yang Feng Shui is about 理 (Theory), 气 (Energy), 形 (Forms), 数 (Calculation).
Landform Theory (形法)
Ling Shen / Zheng Shen （零神 / 正神）
Ci Xiong （雌雄）
5 Elements （五行）
Luo Shu （洛书）
Early Heaven / Later Heaven Ba Gua （先天八卦 / 后天八卦）
Incoming and Outgoing Qi
Incoming and Outgoing water
8 Mansions School (八宅派)
8 Characters School (八字命理派)
San He School (三合派)
Flipping Gua School (翻卦派)
Purple White School (九星飞泊派 / 紫白诀)
Flying Stars (飞星派)
Xuan Kong Da Gua (玄空大卦派)
Twenty-Eight Constellations (二十八星宿派)
Great San Yuan (大三元派)
…and many more…
Some fengshui schools did not apply all of the previously-mentioned theories. It is not appropriate to use just one or some of the schools to do readings and suggest remedies; that will be playing around with fire
A Professional Feng Shui Practitioner must be able to read the landform and apply the correct theories of the Period and Time, then choose an auspicious date and time to remedy and enhance the environment.
YIN FENGSHUI （阴宅)
Again, it is not about mere formulas.
Yin Feng Shui is about 穴 (Dragon Spot), 龙 (Dragon), 砂 (Hills), 水 (Water), 向 (Facing).