High power impulse magnetron sputtering (HiPIMS) discharges have become an important tool for the deposition of thin, hard coatings. Such discharges are operated at a very low working gas pressure in the order of 1 Pa. Therefore, elastic collisions between ions and other heavy particles are often calculated to occur with low frequency, using the hard sphere approximation. However, inside the magnetic trap region of the discharge, a very dense plasma is created and Coulomb collisions become the dominant collision process for ions. In this article, we show that Coulomb collisions are a necessary part of a complete description of ion movement in the magnetic trap region of HiPIMS. To this end, the velocity distribution function (VDF) of chromium and titanium ions is measured using high-resolution optical emission spectroscopy. The VDF of those ions is then described using a simple simulation which employs a direct simulation Monte Carlo scheme. The simulation describes the self-relaxation of the VDF that is initially a Thompson distribution as being created during the sputtering process. Measurement positions inside the discharge are matched to the simulation results choosing an appropriate relaxation time. In this fashion, excellent agreement between simulation and measurement is obtained. We find, that the distribution quickly becomes mostly Maxwellian with a temperature of 9 eV for titanium ions and 4.5 eV in the case of chromium ions. Only the high energy tail of the VDF retains the shape of the initial Thompson distribution. The observed high temperature is explained with an energy redistribution from the highly energetic Thompson distribution into an partly-thermalized Maxwell-like distribution. Finally, the temperature resulting from this energy redistribution is calculated using a simple analytical model which shows good agreement with the measurements.