Difference is in a total spin of an exciton. Let's assume you excite a Pi-electron system which in it's ground state has even number of electrons with total spin 0. If you excite electron by a photon allowed transition would be those which conserve the spin. Now you are in an excited singlet state (S is zero) and photon emission is governed by the same selection rules as it was for absorption previously, emission is highly probable so you have fast (+-~ns) fluorescene. If in excited state spin flip you'll have a triplet state with typically lower energy. Optical transition is prohibited and lifetime is several orders of magnitude larger, this is called phosphorescence.
For reading I would recommend Principles of Fluorescence Spectroscopy by
I want to add some info about photodegradation under exitation of Luminescence (It is general name for photofluorescence and phosphorescence both) photochemical degradation takes place by all means. The more is exitation doze (intensity multply time) the more is degradation of molecules and as a rule with participation of dissolved air oxigen. So magnitude of doze must be small as itis possible expecially at high intensity.