Tithi
A lunar day — the time the Moon takes to gain 12° on the Sun.
A tithi is not a day. It is the interval in which the Moon gains twelve degrees of longitude on the Sun, so it runs anywhere from about 19 to about 26 hours. That is why a tithi can start mid-morning and end the next afternoon, why one can be skipped entirely (kshaya), and why two calendars can honestly name different civil days for the same festival — they are answering 'which day carries this tithi?' with different rules.