Difference between Scattering and Fluorescence It is often said that substances, objects have color because they selectively absorb all color of sunlight except one. The wavelength that is not absorbed reaches our eyes and we perceive it as "color".
This "color" phenomenon is often described as light of a certain wavelength being reflected. I think it is more appropriate to call it scattering.
Scattering is one thing and fluorescence is another. Both processes can give a substance "color". 
I have some "yellow" powder that is fluorescent and its fluorescent color is green....
Scattering, deep down, is not a classical wave phenomena either. It still deals with molecules and atoms absorbing photons and emitting photons....
In essence, what is the difference between scattering (elastic or nonelastic) and fluorescence from an electronic transition point of view?
Best,
Kavan
 A: Reflection can be calculated in a completely classical way requiring only that the material have a bulk polarisibility. It's true that ultimately the polarisibility is a result of the electron configuration, and this arises from quantum mechanics, but you would not call reflection a quantum process any more than you'd call viscosity of a fluid a quantum process.
By contrast, fluorescence is exclusively quantum because it requires electrons to be excited into a higher energy state, then lose some of their energy in lattice interactions and settle to a lower level state. The emission is then from electrons dropping from this slightly lower energy state to the ground state. This is why the fluorescence wavelength is always lower than the wavelength of the incident light.
A quick note on terminology, you say:

what is the difference between scattering (elastic or nonelastic) and fluorescence from an electronic transition point of view

but fluorescence is inelastic scattering, while reflection is elastic scattering (specifically coherent elastic scattering). Fluorescence is inelastic because light is absorbed in an electronic trasnition and some of the energy lost to the lattice. Reflection is elastic because it does not involve an electronic transition and no energy is lost.
A: 
In essence, what is the difference between scattering (elastic or nonelastic) and fluorescence from an electronic transition point of view?

Elastic scattering of photons  happens on the collective  spill over electric field of the material and the quantum mechanical formulation  is comparable with the classical formulation as far as the directionality of the scatter goes. There is no need to invoke quantum mechanical formulations.
One has a quantum mechanical  interpretation  for inelastic scattering, that of absorption of the incoming photon  and ending up at a high energy level and re emission of photons from de excitation to lower energy levels.
If inelastic scattering happens on a material which does not fluoresce  it means that the photon was absorbed and : either the energy goes to vibrational levels or another photon  was re-emitted , or more photons  cascade down,  but the emitted photons are not in the visible range, rather  they are in the  infrared, finally ending in heat.
On a material that fluoresces, the lifetime  is longer and thus the re emission can be observed. In addition each individual atom becomes a source of light and thus the directionality of the incoming beam ( seen in elastic scattering) is lost.

There exist also phosphorescent materials, where the lifetimes  of the energy levels where the photon is absorbed  and the levels it is re-emitted from , are such that the material emits light even when the source is removed for a long time. This depends on the quantum numbers of the energy levels.
