Full classical: physical quantities are scalars (x, p), fields are classical fields (E, B)
Semiclassical (first quantization): physical quantities are now operators.
Full quantum (second quantization): all fields are now field operators.
from wikipedia, second quantization is a misnomer:
> The term "second quantization" is a misnomer that has persisted for historical reasons. At the origin of quantum field theory, it was incorrectly thought that the Dirac equation described a nrelativistic wave function (hence the mistaken "Dirac sea" interpretation), rather than a classical spinor field which, when quantized (like the scalar field), yielded a fermionic quantum field (vs. a bosonic quantum field).
> One is not quantizing "again", as the term "second" might suggest; the field that is being quantized is not a Schrödinger wave function that was produced as the result of quantizing a particle, but is a classical field (such as the electromagnetic field or Dirac spinor field) that was not previously quantized. One is merely shifting from a semiclassical treatment of the system to a fully quantum-mechanical one.