Let's first discuss phenomena in which the wavelength does not change. These are called linear or elastic.
As you point out, reflection, refraction, and scattering all have their origins in the re-direction of light by a medium. In fact, they all have their origins in scattering. As you point out, scattering often means re-direction into any other direction.
When the medium is uniform or homogeneous over lengths that are much larger than a wavelength, the molecules that comprise the medium are excited coherently, that is, all in step with each other. Each molecule re-radiates in step with all the others. In this case the scattered light from each molecule interferes with the scattered light from all the other molecules. It turns out rather remarkably that the field made up of all that scattered light is coherent with respect to the original beam. A well-defined direction of propagation emerges. Refraction.
If the medium is smaller in size than a wavelength, then there are not enough molecules for the scattered field to form a coherent beam. Light goes of in other directions. Rayleigh scattering.
The in-between case, not much smaller than a wavelength, but not much bigger either, is complicated, but the basic principles still apply. Mie scattering.
When the wavelength changes (nonlinear or inelastic) the same comments apply. The only difference is that the medium allows interactions that can remove energy from the light, changing it's wavelength. If the medium is small, we get, for example, Raman scattering. If the medium is large and homogeneous, we get a host of coherent nonlinear phenomena such as Second Harmonic Generation (SHG), Coherent Anit-Stokes Raman Scattering (CARS), and more, in which the re-radiated light goes off in a single, well-defined direction.