Yes, there are two different things that are sometimes called quantization.
First, whenever you put waves in a box (even classical waves) the wavevectors are discrete and sometimes we call this quantization of the wavevector. This does not really involve quantum mechanics -- it is just a statement about the waves that you can fit in a box.
Second you take each wave mode and treat it like a harmonic oscillator and you use quantum mechanics to solve this harmonic oscillator meaning you use energies En = hbar omega (n + 1/2). This really is quantum mechanics.
If you treat these discrete levels of the individual harmonic oscillator with statistical mechanics, the expectation of the "n" in E = hbar omega (n+1/2) at inverse temperature beta is given by the bose factor n_B(beta hbar omega).