Schmidt defines discrete tasks as having a "recognizable beginning and end" (p. 46) and includes throwing, striking a match, and shifting gears while driving as examples.
Serial tasks are composed of a series of discrete tasks, and should be amenable to partitioning or part-task training. Schmidt (p. 46) suggests examples like starting a car, lighting a pipe, playing a piano composition, and performing sequenced routines on an assembly line or in a gymnastics competition.
Continuous tasks have no recognizable beginning and end. Schmidt's (p. 46) examples include running, swimming, or steering a car. It is unclear whether therapists can successfully teach continuous tasks by "breaking them down" or partitioning them.
References:
Schmidt, R.A. (1988). Motor learning and control: A behavioral emphasis. (2nd ed.). Champaign, IL: Human Kinetics.
an unedited Medline search re: discrete and continuous tasks