Raman vs. Brillouin Scattering In my class notes, I have the two types of inelastic scattering described as follows. (Note that the "difference in energy" here is the difference between the incident frequency of the light and the emitted radiation)

Brillouin scattering: The difference in energy generates acoustic phonons
Raman scattering: The difference in energy generates a vibrational oscillation

From what I understood, phonons are vibrations of atoms in a molecule. So what's the difference here? Is there a better way to describe the difference?
 A: In Raman it should say "optical phonon" instead of vibrational oscillation.
I'm not sure if you can call the vibrations in a molecule phonons, since phonons are the vibrations of the lattice in a solid (even when the mathematical description, in first approximation are the same).
A: The distinction isn't actually as sharp as it may seem. If you get really pedantic about it, you can create borderline cases that blur the line as much as you like.
The first answer, that it's just the difference between acoustic phonons and optical phonons, is correct. But then that just leads to the next question: What's the difference between those? In a perfect lattice, it's easy to define: Phonons are quantized lattice oscillations, acoustic phonons are the ones that belong on a continuous band such that the energy goes to zero as the wavelength goes to infinity, and optical phonons are all the other ones.
But what about something that's not a perfect crystal lattice? If you have an imperfect crystal (i.e. every crystal in the actual real universe), then the bands aren't really continuous (the states are very close together, but there's still a finite number of them), and the states of well-defined energy don't quite have a well-defined wavelength. You can have some localized modes associated with defect structures. But you can still unambiguously label the great majority of the modes as either optical or acoustic by identifying the thing as a perturbation of the ideal perfect crystal.
Things get much, much messier as you get into nanocrystalline and eventually amorphous materials, and some people prefer to throw out the concept of a phonon altogether, but this has always seemed excessive to me. To me, a phonon is a quantized oscillation that primarily involves the motion of the ion cores, regardless of whether the structure is periodic or not (and there's a lot of literature out there about "phonons in amorphous materials" that agrees with me). If you get extremely pedantic about that definition, in fact, you have to admit that there aren't actually any phonons in the real world, because there aren't any perfect crystals in the real world. Not useful.
Then you just reduce the size of the system in this thought experiment. What's the fundamental difference between a large molecule and a small amorphous solid? There really isn't one. As you make it smaller, the approximation that lets you treat each quantized oscillation (whether you're willing to call it a "phonon" or not) as part of a continuous band gradually gets worse and worse, and for a small molecule it makes no sense at all.
So I propose this more general definition: A quantized oscillation is described by a displacement field, giving the amplitude of oscillation at each point in the material (or molecule). If the vector difference of this displacement field between any two bonded atoms is a small fraction of rms displacement of all the atoms, the mode is called acoustic. Otherwise it's called optical. For small molecules there may well be no acoustic oscillations, but for a sufficiently large molecule there will be.
So now we're just left with how we define "a small fraction." That's what I mean by the dividing line not being as sharp as you might think.
A: Brillouin scattering is caused by an interaction between light and lattice phonon modes.
Raman scattering is caused by an interaction between light and molecular vibrations.
The key difference is that phonon modes are a collective, long-range phenomenon involving billions or more atoms, whereas molecular vibrations are localized vibrations of a single molecule, which typically only has 2 to 20 atoms.
