Cold atmospheric pressure helium plasma jets are increasingly used in many processing applications, due to a distinct combination of their inherent plasma stability with excellent reaction chemistry often enhanced downstream. Despite their widespread usage, it remains largely unknown whether cold atmospheric plasma jets maintain similar characteristics from breakdown to arcing or whether they possess different operating modes. In addition to their known ability to produce a fast moving train of discrete luminous clusters along the jet length, commonly known as plasma bullets, this paper reports evidence of two additional modes of operation, namely a chaotic mode and a continuous mode in an atmospheric helium plasma jet. Through detailed electrical and optical characterisation, it is shown that immediately following breakdown the plasma jet operates in a deterministic chaotic mode. With increasing input power, the discharge becomes periodic and the jet plasma is found to produce at least one strong plasma bullet every cycle of the applied voltage. Further increase in input power eventually leads to the continuous mode in which excited species are seen to remain within the inter-electrode space throughout the entire cycle of the applied voltage.Transition from the chaotic, through the bullet, to the continuous modes is abrupt and distinct, with each mode having a unique set of operating characteristics. For the bullet mode, direct evidence is presented to demonstrate that the evolution of the plasma jet involves a repeated sequence of generation, collapse and regeneration of the plasma head occurring at locations progressively towards the instantaneous cathode. These offer previously unavailable insight into plasma jet formation mechanisms and the potential of matching plasma jet modes to specific needs of a given processing application.