The term Abazgi refers to both the Abaza

Abazins

The Abazins are a people who live mostly in Karachay-Cherkessia and Adygea of Russia.An Abazin diaspora exists in Turkey, Jordan, Syria, Egypt , and other Islamic countries, most of which are descendants of refugees from the Caucasian War...

 and Abkhaz

Abkhaz people

The Abkhaz or Abkhazians are a Caucasian ethnic group, mainly living in Abkhazia, a disputed region on the Black Sea coast. A large Abkhazian diaspora population resides in Turkey, the origins of which lie in the emigration from the Caucasus in the late 19th century known as Muhajirism...

 as if they were all one people. It was once the preferred designation, but has now been replaced mainly by the two subdesignations.

The literary dialects of Abkhaz and Abaza are simply two ends of a dialect continuum

Dialect continuum

A dialect continuum, or dialect area, was defined by Leonard Bloomfield as a range of dialects spoken across some geographical area that differ only slightly between neighboring areas, but as one travels in any direction, these differences accumulate such that speakers from opposite ends of the...

. Grammatically, the two are very similar; however, the differences in phonology are substantial, and are the main reason why many other linguists prefer to keep the two separate. Most linguists (see for instance Chirikba 2003) believe that Ubykh

Ubykh language

Ubykh or Ubyx is an extinct language of the Northwestern Caucasian group, spoken by the Ubykh people...

is the closest relative of the Abkhaz-Abaza dialect continuum.