In most contexts for time differences, a "day" is a time interval (24 hours) instead of a "concrete thing".

If my job contract says that there has to be "one day between" my resignation letter and my handing back my badge, then it means I can resign on Monday and give back the badge on Tuesday (the next day ; "one day after" ; because "one day" has elapsed). Not Monday/Wednesday. Otherwise "zero days between" these events would mean Monday/Tuesday (with your math) and Monday/Monday is also zero?

But I guess we're just rehashing the old argument on whether indexes should start at zero.