Aerobic activity (as defined in your textbook) is any activity for which the body can supply enough oxygen to allow you to continue to be active for long periods. By this definition, walking, watching TV, playing computer games, and playing a musical instrument are aerobic activities because your body can supply enough oxygen to allow you to do them for a long time.
Active aerobic activity (as defined in your textbook) is an aerobic activity that is intense enough to elevate your heart rate into the aerobic target zone. Active aerobics are good for building cardiorespiratory fitness. Activities generally considered active aerobics can be done at a low intensity so that they fall below the aerobic target zone, in which case they would be aerobic but not active aerobics. For example, swimming slowly is an aerobic activity but is not an active aerobic activity. When swimming is performed vigorously enough to elevate the heart rate into the target zone, it is an active aerobic activity.