Suppose a resident puts on khuffs at 7:00 AM after wudu and breaks wudu at 1:00 PM. The 24-hour period is measured from 1:00 PM, not from the time of donning.
For a legal traveller, the duration is 72 hours measured from the first minor impurity after donning. The distinction is between the time of wearing and the time the original wudu broke.