The paper presents research on chloride minerals of natural origin from Kłodawa (Poland), i.e., colorless, blue and purple halite as well as colorless sylvite. Selected samples of minerals were studied by chemical analysis (ICP-OES, ICP-MS, titration methods) and crystallographic measurements. Then, for the tested halides, research was carried out using far-infrared spectroscopy. Spectroscopic studies confirmed the simple way of distinguishing NaCl and KCl minerals using far-infrared spectroscopy, known in the literature. The novelty is that the article presents for the first time the experimental far infrared spectra of natural blue and purple halite. It was observed that the blue (178 cm−1) and purple (176 cm−1) halites have the strongest infrared band slightly shifted towards higher wavenumbers compared to colorless halite (174 cm−1). As part of the work, the infrared spectra of the crystal structure models of sodium and potassium chloride were calculated for the first time using the density functional theory (with the B3LYP functional and the 6-31G* basis set, 125-atom model). The proposed approach can be used not only as a powerful method differentiating NaCl and KCl minerals, but it can also help with understanding of different defects in crystal lattices for naturally occurring halides and crystals of other minerals.