Aftershocks observed over time scales of minutes to months following a main shock are plausibly triggered by the static stress change imparted by the main shock, dynamic shaking effects associated with passage of seismic waves from the main shock, or a combination of the two. We design a direct test of static versus dynamic triggering of aftershocks by comparing the near-field temporal aftershock patterns generated by aseismic and impulsive events occurring in the same source area. The San Juan Bautista, California, area is ideally suited for this purpose because several events of both types of M ~ 5 have occurred since 1974. We find that aftershock rates observed after impulsive events are much higher than those observed after aseismic events, and this pattern persists for several weeks after the event. This suggests that, at least in the near field, dynamic triggering is the dominant cause of aftershocks, and that it generates both immediate and delayed aftershock activity.