Both phenomena involve the emission of photons shifted in frequency relative to the incident light, because of some energetic transition between states that the system undergoes. As far as I can tell, fluorescence is caused by ionization of the atomic electrons while Raman scatterings agitate phonon modes - but technically speaking, aren't they effectively the same?
I think that it is important to recognize the practical difference between Raman scattering and fluorescence.
If the energy of the photon is resonant with some molecular transition (meaning that it is equal to the energy difference between ground energy state and one of the excited states of the molecule), that the molecule can absorb this photon undergoing energy transition. Now, there are many things that can happen with the molecule in this excited state: it can lose some or all of its extra energy in collision with another molecule, it can fall apart if this extra energy is large enough or - if it avoids these things - it can emit extra energy as a photon which is called fluorescence. The energy of the emitted photon is not necessarily equal to the energy of the absorbed photon as the molecule can end up in a different energy state (for example, having more vibrational energy).
There is a reason that Raman process is called scattering. It is a non-resonant process so the energy of the photon is not important (although higher energies are more efficient in inducing Raman scattering). You can imagine molecule as a small antenna which receives electromagnetic radiation and can re-radiate this. In most cases, the molecule will scatter exactly the same energy - this is called Rayleigh scattering. In few cases, small part of this energy is stored in molecular vibration, or, if molecule is vibrationally excited, it can give this extra energy to the photon. When this happens, scattered light has a shift in wavelength and the process is called Raman scattering.
In contrast to fluorescence, there is no excited state in Raman scattering, therefore the process is almost instantaneous, whereas fluorescence has characteristic lifetime of nanoseconds. So, no matter how one can play with words, these two are very different processes and they totally deserve different names.
Maybe the difference is really just terminology, but we normally think of Raman spectroscopy as the excited state decaying to a vibrationally excited state by emitting a photon of reduced frequency, and the vibrationally excited state then decays by interaction with the lattice. In fluorescence it's the other way around. The excited state decays to a lower energy state by interaction with the lattice and this lower excited state then decays by emission of a photon.
Because of the difference order of interactions you'd expect the delay between absorption and emission to be shorter for Raman scattering than for fluorescence. Indeed there's a gradation between fluorescence and phosphorescence, and the lifetime for phosphorescence can be many seconds.
Raman spectroscopy and fluorescence are two different phenomena in the sense that in Raman scattering the incident photon is not fully absorbed and perturbs the molecule exciting or de-exciting its vibrational or rotational energy states. But in fluorescence the photon is completely absorbed causing the molecule to jump to a higher electronic state. Fluorescence occurs due to real electronic transitions. On the other hand, Raman scattering occurs as a result of virtual electronic-vibrational transitions .More generally, we can say that fluorescence is an absorption or re-emission process and Raman scattering is an inelastic scattering process.
If a photon outward to a particle is the same as the photon inward to the same particle, but the energy of the photo is different between inward and outward, we can say the photon is scattered by that particle. In fluorescence, a particle absorbs a photon which cause the electronic state of the particles to a excited state, then emits a new photon by relaxation.
Scattering is phenomenon of deviation from its trajectory due to non-uniformities in medium through which it is passing. Eg. When a ball is deviated by tennis bat due to its motion.
Flourescnce is consuming the photon, and emitting back lower energy photon.