Diwali is celebrated during Ashvin and Kartika, the two Hindu lunisolar months associated with its regional calendar systems.
The apparent two-month answer reflects the distinction between the amanta and purnimanta traditions. In the amanta system, the lunar month ends on the new moon, so the main Diwali observances fall around the end of Ashvin and the beginning of Kartika. In the purnimanta system, the same festival period is identified within Kartika.
Diwali is not tied to a fixed Gregorian date. It generally occurs between mid-October and mid-November and is centered on the new moon, or amavasya. The five-day sequence includes Dhanteras, Naraka Chaturdashi, Lakshmi Puja or Kali Puja, Govardhan Puja, and Bhai Dooj, with regional variations.
This is why sources may name Ashvin, Kartika, or both without describing different festivals. The question’s pairing captures the calendar variation rather than a disagreement about when Diwali is observed.