Observations from the Hinode/XRT telescope and STEREO/SECCHI/EUVI are utilized to study polar coronal jets and plumes. The study focuses on the temporal evolution of both structures and their relationship. The data sample, spanning April 7-8 2007, shows that over 90% of the 28 observed jet events are associated with polar plumes. EUV images (STEREO/SECCHI) show plume haze rising from the location of approximately 70% of the polar X-ray (Hinode/XRT) and EUV jets, with the plume haze appearing minutes to hours after the jet was observed. The remaining jets occurred in areas where plume material previously existed causing a brightness enhancement of the latter after the jet event. Short-lived, jet-like events and small transient bright points are seen (one at a time) at different locations within the base of pre-existing long-lived plumes. X-ray images also show instances (at least two events) of collimated-thin jets rapidly evolving into significantly wider plume-like structures that are followed by the delayed appearance of plume haze in the EUV. These observations provide evidence that X-ray jets are precursors of polar plumes, and in some cases cause brightenings of plumes. Possible mechanisms to explain the observed jet and plume relationship are discussed.