Both fluorescence and phosphorescence are extremely beautiful chemical phenomena that practically everyone has experienced at one point or another. Explaining their origins (which in turn will explain the difference between the two) gets a bit technical, but if you can sufficiently break down a complex subject into something anyone can understand, it demonstrates that you have a high degree of knowledge of the material. So, here goes!
Certain materials (dyes, in particular) can “absorb” light. This absorption (also called “excitation”) sends a dyes electron that was happily resting in a low, stable energy-state (the so-called “ground state”) into an excited-state. This happens extremely rapidly, on the order of 10^-15 seconds. The electron wants to get back to stable ground as soon as possible, and rapidly (over 10^-14 sec to 10^-11 sec) reaches a somewhat stable energy level known as the “LUMO” in chemical slang (Lowest Unoccupied Molecular Orbital). From there, it has several choices.
The electron could simply fall back to the ground state without putting out any light whatsoever, dissipating its extra energy as heat. This would be pretty dull, and these processes (quenching, non-radiative relaxation) don’t contribute to either fluorescence OR phosphorescence. However, there are two other possibilities. The electron could fall back down to the ground state along with the emission of light. This process, fluorescence, happens over the time scale of 10^-9 to 10^-7 seconds. The color of light that is emitted depends on the energy difference between the LUMO and the ground state.
Where have you seen fluorescence? Anytime you’ve shone a black light on someones skin at a party and seen wild tattoos they’ve painted on with fluorescent paint, you know you’re dealing with fluorescence. The light from the “black” light is of an appropriate frequency to send electrons in the paints dye soaring into the excited state, and the electrons resulting fall back to stable ground is shown by the display of light.
Besides falling back to the ground state and giving off energy (either as heat, or light), there is a third possibility: through a process known as “intersystem crossing”, the electron that’s at the LUMO trying to make up its mind can travel to a slightly lower level and hang out there for a while. This level is called the “excited triplet state” (T1) and it’s special because it’s unusually stable, compared to the rest of the electrons which are whizzing around. The electron resides at the T1 state for 10^-3 or so seconds and then falls back down to the ground state, giving off light much in the case of fluorescence. This is called phosphorescence.
The critical difference between the two is that fluorescence is fast, and as soon as you remove the source of excitation (black light), the resulting light emission halts. However, anyone who has seen items that “glow in the dark” when “charged up” by holding them up to a bright light for a few seconds has witnessed the slower phenomenon of phosphorescence. The two are related, but they take completely different paths throughout their journey.
Anyone wishing to learn more about this subject is encouraged to read a good book on optical chemistry and to also find a decent copy of what’s known as a “Jablonski energy diagram”, which lays everything out relatively nicely.