Luminescence can be defined as the radiation emitted by a molecule or an atom on return to ground state from excited state after initial absorption of energy. Both fluorescence and phosphorescence are type of photoluminescence which involves absorption of energy and excitation of atom to higher energy level followed by emission of electromagnetic radiation (or return to low energy state). In both, the emitted photon (light) has lower energy than the absorbed photon and emission occurs at a longer wavelength than the incident light. The major difference is the duration for each process to occur after the initial absorption of light of correct wave length.
Fluorescence vs Phosphorescence

Fluorescence
Phosphorescence
It is the absorption of energy by atoms or molecules followed by immediate emission of light or electromagnetic radiation
It is the absorption of energy by atoms or molecules followed by delayed emission of electromagnetic radiation
The emission of radiation or light suddenly stops on removal of source of excitation
The emission of radiation remains for some time even after the removal of source of excitation
In Fluorescence, the excited atom has comparatively short life time before its transition to low energy state
In Phosphorescence, the excited atom has comparatively long life time before its transition to low energy state
The time period or interval between the absorption and emission of energy is very short
The time period or interval between the absorption and emission of energy is comparatively long
Absorption process occurs over short time interval and involves the transition from ground state to singlet excited state and do not change the direction of the spin.

Phosphorescence involves the transition from the single ground energy state to excited triplet state and involving a change of spin state
The emitted photon (light) has lower energy than the absorbed photon and emission occurs at a longer wavelength than the incident light
The emitted photon (light) has lower energy than the absorbed photon and emission occurs at a longer wavelength than fluorescence
In fluorescent materials, gives an ‘an immediate flash or afterglow’ on excitation
Phosphorescent materials appears to 'glow in the dark', because of slow emission of light over time. 
Examples of Fluorescence:
Gemstones fluoresce, including gypsum, talc.
Jelly fish, chlorophyll extract, vitamins etc
Examples of Phosphorescence:
Glow of clock dial or toys or in bulbs after switching off the light in the room. The glow remains for some minutes or even hours in a dark room
Phosphorescent materials in sign board illuminate during night.

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