Terminology referring to the term "quantization" in Schrödinger and Dirac equation

Question

When people write "Quantization of Dirac equation" is the word "Quantization" the same as "second quantization"? As I understand it, both Schrödinger and Dirac equations describe one particle (or many specific number of particles using tensor product) and when we "quantize the equation" we introduce a formalism that can describe creation and annihilation of particles.

Is this correct?

Answer 1

Yes, the two equations describe quantum particles, i.e., the "first quantization" is already done, and the only further quantization possible is second. (Note how it is different for photons, which are classically already described by a wave equation, see this discussion.)