Level triggering and edge triggering are distinct concepts in digital circuits, with level triggering responding to a specific voltage level while edge triggering activates on the rising or falling edge of a signal. Level-triggered devices, like JK flip-flops, can operate effectively with slow signal transitions, unlike edge-triggered devices that require a minimum rate of change. Additionally, some devices allow users to select whether they trigger on the rising or falling edge, as noted in the specifications of certain binary counters. The CD4020 and CD4040 counters, for example, trigger on the falling edge of the clock pulse but can reset on a rising signal. Understanding these differences is crucial for designing reliable digital systems.