What are different types of nail polish?

Up till recently, conventional nitrocellulose nail polishes were all that existed. These consisted of a petrochemical solvent (like Toluene, Butyl Acetate, etc) with plasticizers and other ingredients to add properties (like film flexibility). There are now water based polishes that exist, like Acquarella, SunCoat and Honeybee Gardens that are much safer due to the absence of petrochemical solvents.