We use an ionization region model to explore the ionization processes in the high power impulse magnetron sputtering (HiPIMS) discharge in argon with a titanium target. In conventional dc magnetron sputtering (dcMS), stepwise ionization can be an important route for ionization of the argon gas. However, in the HiPIMS discharge stepwise ionization is found to be negligible during the breakdown phase of the HiPIMS pulse and becomes significant (but never dominating) only later in the pulse. For the sputtered species, Penning ionization can be a significant ionization mechanism in the dcMS discharges, while in the HiPIMS discharge Penning ionization is always negligible as compared to electron impact ionization. The main reasons for these differences are a higher plasma density in the HiPIMS discharge, and a higher electron temperature. Furthermore, we explore the ionization fraction and the ionized flux fraction of the sputtered vapor and compare with recent experimental work.

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