Temporal evolutions of the ground state number densities of titanium atoms and ions and the ionised density fraction during pulse on-time are experimentally investigated for the high-power impulse magnetron sputtering process in an Ar and Ar/N2 atmosphere. For the study, two distinct pulses with the same pulse length at a constant average power but different pulse off-times were selected. In both conditions, four representative points within the hysteresis curve were chosen, and the time evolutions of sputtered species densities were investigated in both the target and the substrate regions. At the pulse beginning, a high density of residual particles sputtered during the previous pulse is present in both studied regions. In the target region, in conditions of longer pulse off-time and thus higher peak discharge current, 95% of sputtered particles are ionised in metallic, transition and compound regimes. With shorter pulse off-time conditions, and thus a lower peak discharge current, the ionised density fraction is the lowest in the metallic regime; in the transition and compound regimes, it exceeds 80%. In the substrate region, the temporal evolution of sputtered species densities differs from that obtained in the target region. After the pulse ignition, titanium atoms and ions remaining near the substrate from the previous pulse are pushed away. In the metallic regime, the sputtered atoms refill the substrate region already during the pulse on-time in both the low- and high-current conditions. In the high-current conditions, the titanium ions arrive at the substrate together with the sputtered atoms; however, in the low-current conditions, the titanium ion density decreases during the pulse on-time, and the titanium ions arrive later during the pulse off-time. In the transition and compound regimes, both densities steadily decrease during the pulse on-time and the titanium atoms and ions arrive at the substrate during the pulse off-time.