Behind the observance sits a piece of arithmetic. A tithi is the time the Moon takes to open a further twelve degrees of separation from the Sun. Chaturdashi occupies the arc from 156 to 168 degrees of that separation. The Moon does not move at a fixed rate, and the same twelve degrees may take a little over nineteen hours near perigee or close to twenty six near apogee. A calendar has to name whole days, so the rule is that whichever tithi is current at sunrise gives the day its name. A tithi shorter than the interval between two sunrises can therefore be skipped entirely, which the tradition calls a kshaya tithi, and one longer than that interval can carry its name over two civil days, an adhika or vriddhi tithi. Both occur in the ordinary course of a year, and both are why an observance can appear on two dates in the same almanac.
Each tithi is halved again, and each half carries a karana, so the first half of Chaturdashi carries Gara, the fifth, and the second Vanija, the merchant's karana. Seven of the eleven karanas repeat, cycling eight times through the month, while four are fixed to particular half tithis at the month's opening and close.
The Moon is waxing through this arc, setting later each evening and carrying about 98 per cent of the disc lit, all but full to the eye. That figure is a consequence of the definition rather than an observation added to it: elongation fixes the phase, so naming the tithi already names how much of the disc is lit.