Wikipedia:WikiProject Aztec/Terminology

"Aztec" is a term used to refer to certain ethnic groups of central Mexico, particularly those groups who spoke the Nahuatl language and who achieved political and military dominance over large parts of Mesoamerica in the 14th, 15th and 16th centuries, a period referred to as the Late post-Classic period in Mesoamerican chronology.

Often the term "Aztec" refers exclusively to the people of Mexico-Tenochtitlan, situated on an island in Lake Texcoco, who called themselves Mexica Tenochca or Colhua-Mexica.

Sometimes it also includes the inhabitants of Tenochtitlan's two principal allied city-states, the Acolhuas of Texcoco and the Tepanecs of Tlacopan, who together with the Mexica formed the Aztec Triple Alliance which has also become known as the "Aztec Empire". In other contexts it may refer to all the various Nahua city states and their peoples, who shared large parts of their ethnic history as well as many important cultural traits with the Mexica, Acolhua and Tepanecs, and who like them, also spoke the Nahuatl language. In this meaning it is possible to talk about an Aztec civilization including all the particular cultural patterns common for the Nahuatl speaking peoples of the late postclassic period in Mesoamerica.

Aztec
"In Nahuatl, the native language of the Aztec, 'Azteca' means 'someone who comes from Aztlán', a mythical place in northern Mexico. However, the Aztec referred to themselves as Mexica (IPA ) or Tenochca and Tlatelolca according their city of origin. Their use of the word azteca was like the modern use of Latino, or Mediterranean: a broad term that does not refer to a specific culture."

Aztlan

 * Aztlan refered to someone who comes from the mythical Aztlan, and this should apply to the nahua tribes that lived in the Anahuac valley. Meshicas (Tenochcas and Tlatelolcas) were the last tribe to arrived.

Mexica
"The modern usage of the name Aztec is applied specifically to the Mexica peoples of Tenochtitlan, suggested by Alexander von Humboldt and adopted by Mexican scholars of 19th century, as a way to distance 'modern' Mexicans from pre-conquest Mexicans."

"'Mexica', the origin of the word Mexico, is a term of uncertain origin. Very different etymologies are proposed: the old Nahuatl word for the sun, the name of their leader Mexitli, a type of weed that grows in Lake Texcoco. The most renowned Nahuatl translator, Miguel León-Portilla, suggests that it means 'navel of the moon' from Nahuatl metztli (moon) and xictli (navel) or, alternatively, it could mean navel of the maguey (Nahuatl metl)."

Origin and meaning of the word Mexica
"Mexica is a term of uncertain origin. Some say it was the old Nahuatl word for the sun. Leon Portilla suggested:

"México significa "Ombligo de la Luna" en Náhuatl. Esta palabra viene de Mexitli que esta compuesta de metztli (Luna) y xictli (ombligo)."

the official meaning is:

el origen de la palabra es que deriva de de Mexictli, nombre dado al dios Huitzilopochtli, "el colibrí del sur" que condujo a los mexicas hacia la región lacustre de centro de México. Mexictli se compone de las raíces metl (maguey), xictli (ombligo) y el locativo co, su traducción sería "en el ombligo del maguey", lo cual nos habla del sentido mitológico que a esta planta le dieron las culturas prehispánicas.

Mexico means "The Navel of the Moon" in Nahuatl. This word comes from "mexitli" that is made up of "metztli" (moon) and "xictli" (navel).

The origin of the word derives itself from "Mexictli", the name given to the god Huitzilopochtli "the hummingbird of the south" that conducts the Mezicans to the "lacustre" region in the center of Mexico. Mexictli is composed of the roots "metl" (maguey, a type of cactus), "xictli" (navel) and the locative "co", its translation would be "the navel of the maguey", which tells us of the mythological sense that the prehispanic cultures gave to this plant.

the Aztec term is a general one that refers to the Chichimecs, Acolhua, Tepanecs, and the Mexica, once they reached the valley, the "aztec" ceased to exist, culturally, liguistically, ethnically and politically. Seeing

Mexica vs. Aztecs
Mexica

Moctezuma vs. Montezuma vs. Motecuhzoma
Moctezuma

Tlaxcalans vs. Tlaxcalteca
Tlaxcalans