Q:

Scattering vs Stimulated Emission

I am currently reading Practical Flow Cytometry, fourth edition, by Howard M. Shapiro. The author says the following when discussing scattering:

Scattering, which explains both reflection and refraction, typically involves a brief interaction between a photon and an electron, in which the photon is annihilated, transferring its energy to the electron, which almost immediately releases all of the energy in the form of a new photon. Thus, light scattered by an object has the same (or almost the same) wavelength, or color, as the incident light.

This reminded me of stimulated emission. But I remembered that, in photonics (such as the case of solid state lasers), the wavelength of the emitted light is different from that of the incident light (for instance, when a laser diode of some wavelength is used to pump some gain medium, which then emits light of totally different wavelength). So I sought to do further research to clearly understand the difference between these two phenomena.
Wikipedia describes stimulated emission as follows:

Stimulated emission is the process by which an incoming photon of a specific frequency can interact with an excited atomic electron (or other excited molecular state), causing it to drop to a lower energy level. The liberated energy transfers to the electromagnetic field, creating a new photon with a phase, frequency, polarization, and direction of travel that are all identical to the photons of the incident wave. This is in contrast to spontaneous emission, which occurs at random intervals without regard to the ambient electromagnetic field.

Surprising to me, this description seems to agree with that of scattering, in which the new, emitted light has the same wavelength (since wavelength is proportional to frequency) as the incident light. But this seems to contradict with what I know about how stimulated emission works in the context of photonics.
So what am I misunderstanding here? Doesn't stimulated emission emit light of different wavelengths, depending on the medium/material? What is the difference between scattering and stimulated emission? I would greatly appreciate it if people would please take the time to clarify this.

A:

In the case of scattering the incident photon isn't (usually) interacting with an excited electron, so we don't have the basic requirement for stimulated emission.
In the case of scattering the incident photon is absorbed, raising the electron's energy level (in an atom or molecule). The electron spontaneously drops down from this level to its original level (in the simplest case), emitting a single photon of the same frequency as the original photon. This emitted photon does not (except by chance) have the same phase, polarisation direction or propagation direction as the incident photon – very different from stimulated emission.

