Well, this is a debate on semantics again. It depends a bit on the subject you are discussing, what you call "semiclassical". In atomic physics and quantum optics usually semiclassical refers to the approximation that the matter (electrons, atoms, molecules, condensed matter) is treated with quantum theory and the electromagnetic field as a classical field. It's amazing, how much can be described with this semiclassical model. Often the quantization of the em. field is only a small correction. An important example is the photoelectric effect, which is not proving em.-field quantization but is well described in the "semiclassical approximation" in this sense.
You can also consider the opposite approximation, i.e., you have a classical charge-current-density distribution and consider the quantized em. field coupled to it. For an oscillating charge distribution you then get coherent states of the quantized electromagnetic field, which shows that classical em. waves (light) is not a naive stream of photons but a highly non-trivial quantum superposition of states with all photon numbers (the coherent state). Itzykson and Zuber call this approximation "hemiclassical" to distinguish it from "semiclassical", but I've never seen any other text using this convention.
Of course, you can also ask, in how far a quantum system can be approximated by classical physics. E.g., a quantum particle like an electron interacting with a (classical) electromagnetic field in non-relativistic QM can be described by the Schrödinger equation, and this equation can be solved using "singular perturbation theory", which is formally an expansion in powers of ##\hbar## (starting with the singular term ##\propto 1/\hbar##, which corresponds to the classical limit, leadking to the Hamilton-Jacobi PDE to describe the motion of classical point particles). This is known as the Wentzel-Kramers-Brillouin (WKB) method and is completely analogous to the mathematically identical treatment of em. waves in classical electromagnetism in powers of the wave length (eikonal approximation), leading to the approximation of wave optics by ray optics. The real fun with this are the classical return points (in QM) or equivalently the boundary of shadows (in classical EM). By the way, this was the way Schrödinger used ingeniously when "deriving" his equation: He thought of classical physics as the eikonal approximation of an equation describing de Broglie's matter waves. Thinking about the Hamilton-Jacobi PDE he realized that the corresponding equation should be his Schrödinger equation. Interestingly he started with the relativistic case and got what's now called the Klein-Gordon equation for scalar bosons. He calculated the hydrogen spectrum and found the wrong finestructure. Since this was known to be a relativistic effect he then went to the non-relativistic case, getting the equation now named after him the Schrödinger equation. There the hydrogen spectrum came out right up to the finestructure which, however, was expected since now it was a non-relativistic theory. The reason for the failure of the Klein-Gordon equation to describe the hydrogen spectrum was of course just that electrons obey the Dirac equation, and doing the calcululation with the Dirac equation indeed gives the correct finestructure.
Ironically in the Bohr-Sommerfeld quantization the naive relativistic treatment of the hydrogen atom, Sommerfeld got the correct finestructure although not knowing about spin at the time at all. For me it's an enigma, why a wrong model with an incomplete treatment of the electron as a spinless particle yields the correct finestructure ;-)).
