Fluorescence, chemiluminescence and phosphorescence are 3 different types of luminescence properties, i.e. emission of light from a substance.
Fluorescence is a property where light is absorbed and remitted within a few nanoseconds (approx. 10ns) at a lower energy (=higher wavelength), while bioluminescence is biological chemiluminescence, a property where light is generated by a chemical reaction of an enzyme on a substrate.
Phosphorescence is a property of materials to absorb light and emit the energy several milliseconds or more later (due to forbidden transitions to the ground state of a triplet state, while fluorescence occurs in excited singlet states). Until recently, this was not applicable to life science research due to the size of the inorganic particles. However the boundary between the fluorescence and phosphorescence is not clean cut as transition metal-ligand complexes, which combine a metal and several organic moieties, have long lifetimes, up to several microseconds (as they display mixed singlet-triplet states).