The present study compares the operation of two cold atmospheric plasma jet (CAPJ) configurations: needle‐to‐cylinder electrode configuration (CAPJ I) and single high‐voltage cylinder electrode around the quartz tube (CAPJ II). The CAPJs were operated in argon flowing through a quartz capillary with 0.5‐mm inner diameter into the ambient air, and the plasma was generated by sinusoidal kHz frequency AC power supplies. The main emphasis of the study was on the mechanism of the initiation of ionization waves for these two configurations. For both CAPJs, there appeared several ionization waves during one half‐period of the applied voltage waveform, and the number of ionization waves increased at higher voltage amplitudes. However, we discovered marked differences in the initiation of the ionization waves for two different CAPJ configuration. The applied voltage controlled the initiation of consecutive ionization waves, which propagated from the grounded electrode towards the tube orifice in CAPJ I. In the case of CAPJ II, certain time had to pass for the initiation of a new ionization wave, and subsequent ionization waves within the same half‐period started at the tube orifice. In addition to the differences in the initiation of the ionization waves, we observed that the CAPJ I was ignited and sustained at lower voltages, while CAPJ II produced a longer plasma jet. The observed advantages and deficiencies of investigated CAPJ configurations point out their potential in different applications.