Languages that have common roots and basic lexicons are grouped into “families” and “super-families”.
The Chechen and Ingush languages make up the Nakh group of languages, which in turn belong to the Nakh-Dagestani language family. The Nakh-Dagestani language family in turn belongs to the Sino-Caucasian super-family, which encompasses other languages such as Basque, Pelasgian (pre-Hellenic language of Greece) and Navajo (spoken by indigenous tribes in USA).
So, it goes Vainakh > Nakh > Nakh Dagestani > Sino-Caucasian.
Nakh-Dagestani language group is indigenous to the Caucasus, having been around in the region for roughly 8,000 years and is the same age as the Indo-European group (from which Spanish, English and Russian have descended).
Interestingly, the Nakh language has no relationship with other Southern Caucasus languages such as Georgian or Turkic which belong to a different language family called Kartevalian.