The language family of the Aztec language, the Ute-Aztec language family, includes languages spoken from Oregon, California, Colorado, and southern Idaho into central Mexico, including the Ute language of the Ute people (namesakes of the state of Utah), the Shoshone language, the Hopi language, and the Aztec Nauhtl language, and the southernmost Pipil language of the Cuzcatlecs people of El Salvador. All the Ute-Aztecan peoples including the Ute, Shoshone, Hopi, Paiute, and Aztec peoples all have a common origin and all descend (at least partially) from the same the proto-Ute-Aztec people who probably lived somewhere in an area including southwestern border USA and north/central Mexico before migrating north into Idaho, California, and Utah, and south into more central Mexico, and west into New Mexico and Texas, with Ute-Azteca speakers believed to have settled in California around 2000 BC.

So basically, related peoples with a significant commonality in origins, but some Ute-Aztecan like the Tarahumara, Cuzcatlec and Aztec peoples are considered 'mexican' and 'indigenous American', whislt the other like the Shoshone, Ute, Paiute, and Comanche are exactly the type of horseback plains Indian warriors Americans and others imagine when they think about Native Americans.

It is also important to note that the Ute-Aztecan people were actually once the dominant ethnolinguistic group and societies in the western United States in addition to Mesoamerica, and include a range of people's and societies ranging from the highly advanced and centralized Aztecs who forged and stood at the head of a massive empire, to Paiute hunter gatherer bands in California, to semi-sedentary Hopi settlements. Areas like southern California, Arizona, New Mexico, Utah, Sonora (Mex), northern Texas, Eastern and southern Oregon and Idaho, Utah, and northern California were all once inhabited by Ute-Aztecan peoples.

As for genetics, the patrilineal y-dna haplogroup makers - Y-chromosome mutations passed from father to son indefinitely - of the Ute-Aztecan people's show that Ute-Aztecan males carry the y-dna marker Q at extremely high levels, peaking at 100% in some groups and around 93-95 % in Aztec males. However, haplogroup Q is the dominant y-dna marker in the whole of the Americas and amongst all indigenous American males, and even Inuit and Greenlandic males carry it at high levels , sometimes reaching 90%. This y-dna marker is even present amongst Saudi Arabian bediouns!

In addition to most Ute-Aztecan males mostly carrying haplogroup Q, they also carry another y-dna marker R1, which is also present throughout the Americas albiet at much lower levels than haplogroup Q, but R1 reaches frequency peaks amongst Algonquin males of Western Canada and the Great Lakes region. Around 20-3% of Ute-Aztecan males carry the R1 haplogroup. However, like haplogroup Q, R1 is also common thoughtout the Americas. Weirdly enough, R1 is also the dominant male y-dna marker in western Europe and western Eurasia and northern India and parts of West Africa.

Also, both haplogroup R1 (and R) and Q males descend from a common patrilienal ancestor marker P, who was probably a guy who lived somewhere in southeast Asia-Pacific region, and his descendants dispersed westwards into Europe and eastwards into the Americas ~30,000 years ago, his descendants including of the ancestral Siberian paleo-Indian colonists of the Americas, the proto-Turkic peoples, and proto-Indo-Europeans. All this makes it very hard to actually associate genetic markers with the early Ute-Aztecan groups and be able to more fully document the spread and migration of the language family and it's speakers and the extent of linguistic assmiliation.

As such however, it is believed that both haplogroup Q and R1 were carried by the Siberian and Central Asian males who were ancestors to the all the indigenous American peoples including the Ute-Aztecans, and that the presence of these markers shows this Siberian/Central Asian descent and not descent from European men.