The term evolutionary track is used for the track over a H-R diagram plotting a star's changes over its lifetime. The term stellar evolution indicates these changes (for a single star or a type of star) rather than like the more "biological" sense of evolution as how successive generations differ. An evolutionary track can be plotted as a curved line from a point plotted for the star at some point in its life (presumably early in its life, such as when it enters its main-sequence phase), leading to a later point in its life (e.g., its core collapse supernova). It might at some point enter the H-R diagram's red-giant region and possibly its asymptotic giant branch region.
Hayashi tracks are a set of such tracks calculated for the pre-main-sequence star phase.