Stop, cease, quit, discontinue, desist are comparable when they mean to suspend or cause to suspend activity.
Stop applies primarily to action or progress or to what is thought of as moving or progressing; cease applies primarily to states and conditions or to what is thought of as being or as having existence; thus, a train stops but does not cease ; the noise it makes both stops and ceases ; one stops a car but may cease driving a car; one stops work on a book but ceases one’s efforts to perfect its style.
Stop frequently connotes a sudden or definite, cease a gradual suspension of activity.
Quit (see also GO ) may suggest finality in ceasing an activity, sometimes with an implication of accepting frustration or failure.
Discontinue implies the suspension of some activity, especially one that has become a form of occupation or employment or is a practice or habit.
Desist usually stresses forbearance or restraint as the motive for stopping or ceasing but it may imply the futility of one’s efforts.