Naraka Chaturdashi, also known as Choti Diwali, is the day before Diwali. It falls on the fourteenth day (Chaturdashi) of the dark half of the month, in Ashwina by the lunar months that end at the new Moon and in Kartika by the months that end at the full Moon. It recalls the defeat of the demon Naraka by Krishna. Many families take an oil bath before sunrise (abhyanga snan), light lamps, and begin the festive meals and sweets.
The date is fixed by the day on which Chaturdashi is in force at sunrise, because the oil bath is taken before sunrise, in the early morning. In some regions, especially in Gujarat, the same Chaturdashi is also kept as Kali Chaudas, a night observance with a puja in the Nishita, the middle of the night. That night can fall on a different civil day from the morning of Naraka Chaturdashi, so the timing column shows the Kali Chaudas night window with its own date where they differ.
Why do cities differ? Chaturdashi begins and ends at one instant worldwide, but sunrise and midnight are at different clock times in each city. The tithi may still be running at sunrise in one city and have ended before sunrise in another, so the morning observance can move by a day, and the night window moves with the local clock.
A calm note: the day is about cleanliness, light and the start of the festive days, and the oil bath and lamps are the heart of it. If your family or temple marks the day differently, follow them. Diwali itself, the next day, has its own page of dates and Lakshmi Puja times.