The probe method for the ion current density measurements and a theoretical calculations of the dynamics of neutral and charged plasma particles by ionization region model (IRM), are used to study high-power impulse magnetron sputtering (HiPIMS) short and ultra-short pulse discharges. The paper studies reasons for the increase in the average ion current density on the substrate at shorter pulses, when the average discharge power does not change. HiPIMS pulses are applied to the copper target at constant values of the average discharge power (1000 W) and the peak current (150 А), respectively, while the pulse time of the discharge voltage ranges from 4 to 50 µs. A power supply with low output inductance is designed to generate ultra-short pulses. It is shown that the discharge pulse time reduction leads to a multiple growth (from 2 to 7 mA/cm2) in the average ion current density onto the substrate and the growth in the peak intensity of Ar+, Cu+ and Cu2+ recorded by optical emission spectroscopy. A theoretical model of this effect is based on the spatially averaged IRM, which takes into account afterglow effects. According to theoretical calculations, the increase in the average ion current density onto the substrate is determined by the plasma dissipation in the ionized region after the pulse end. Also, explained is the decrease in the copper deposition rate from 180 to 60 nm/min with decreasing pulse time from 40 to 4 µs. A comparison of the experimental data and those obtained earlier, shows that the suggested dependences of the ion current density and deposition rate on the HiPIMS pulse time, are typical for discharge systems with different cathode materials and configurations, i.e., for single- and dual-magnetron systems. This indicates to a common nature of the phenomena observed and additionally confirms the results obtained.