Hyperfine splitting is not the same as polarization. Hyperfine splitting is due to a property of quantum particles called spin. This property creates "hyperfine splitting" in the energy levels of quantum systems past the fine structure that arises due to first order relativistic corrections.
Polarization is unrelated. I has to do with photons, which as light waves. They propagate by oscillating electric and magnetic fields in orthogonal planes. The polarization of light has to do with which plane the field is oscillating in.
Hope that helps. If you need more detail, there is certainly loads of it on Wikipedia and they tend to be accurate with their physics pages.