How are florescence and phosphorescence different?

When an atom absorbs energy, its electrons are excited to one of the higher energy states(usually called orbits). The excited electron is not stable at this new place and wants to come back to the original place, where it truly belongs. The electron can do it in more than one ways:

One way to do it is by simply emit the same amount of energy it absorbed and move to the original place. In this case,  it is a simple emission.

Another way to emit energy is to move slightly down within the same energy level. This will cause the energy to lower but the change is so small that the emission of light will not take place during this movement within the same shell. After a slight movement down, the electron can jump to the lower energy level just as in the previous case. Here since the electron already moved down a little bit so the emission will not be as much as absorption but slightly lesser and the phenomenon will be called fluorescence.

A third way to emit radiation comes across when some materials have special valley like states within the same energy level. An electron moves down in an energy state but gets entrapped in a valley in the shell. This valley captures the electron for some time and then allows it to move down to the lower energy level. Since the escape of electron from the valley can take significantly longer time hence often household items that are phosphorescent glow even long after they were irradiated to excite their electrons.