A tithi is a lunar day. It is the time the Moon takes to gain twelve degrees of separation from the Sun. Thirty tithis make one lunar month — from one new moon to the next. Because the Moon’s speed varies along its orbit, a tithi is not a fixed length: it can run anywhere from roughly 19 to 26 hours. That is why a tithi rarely lines up with midnight-to-midnight, why a tithi can begin at 10 pm and end the next evening, and why two consecutive calendar days can carry the same tithi — or a tithi can vanish from the calendar entirely.
Paksha is the half of the month. The thirty tithis divide into two fortnights of fifteen. Shukla Paksha is the bright, waxing half — from the new moon (Amavasya) up to the full moon (Purnima). Krishna Paksha is the dark, waning half — from the full moon back down to the new. Every tithi therefore has a full address: “Bhadrapada Shukla Chaturthi” means the fourth tithi of the waxing half of the month of Bhadrapada — and that address, not a Gregorian date, is what fixes Ganesh Chaturthi.
Which day do we observe, then? Since a tithi can straddle two sunrises, the rule most observances follow is the tithi prevailing at a specific moment — sunrise for many vrats, midday for some, moonrise or midnight for others. This is also why the same festival can fall a day apart in two cities: sunrise itself differs, so the tithi “present at sunrise” can differ. Two panchangs showing different dates can both be right — for their own cities. Our dates are calculated for Delhi-NCR (IST).