Fluorapatite is a Fluorine-Rich member of the Apatite group. It is a Phosphate mineral and is the most abundant form in the Apatite group by a wide margin and was the original mineral called Apatite.
The name Apatite is actually from a Greek word meaning "deceiver" in allusion to the fact that it tends to form in varieties and colors which look like other minerals. It comes from an incredibly wide variety of locales and formations and many individuals collect only forms of Apatite.
Nerd-Fact: Fluorapatite occurs in teeth when exposed to simple fluorine ions which is why we brush our teeth with Fluoride. The presence of Fluorapatite is what helps prevent tooth decay.
What to look for: Color, Luster, Isolation and Formation of Crystals, Internal Clarity, Associations, Specimens on Matrix, Unusual Localities, and, Color Zones.