First, it's important to emphasize that the Maya and Aztecs (Triple Alliance) existed on pretty different timescales. Mayan peoples, communities, and civilizations have existed from before 500 B.C. through modern times. The imperial state that we call the Aztecs only existed from 1428-1521. As you say, the Maya were independent and often competing kingdoms. So when you ask about the relationship between the Aztecs and Maya, we're really only looking at a tiny slice of Mayan history.

The only territorial conquest that the Aztec made in Mayan lands was that of Soconusco. This region, located on the Pacific Ocean near the modern Mexican border with Guatemala, was not a completely Maya region. Instead it "represented a corridor of communication between Mixe-Zoquean speakers to the west, and Mayan to the east" (Kappelman 2004). The exact cultural history and makeup of Soconusco is unclear, but the area was influenced by Mayan characteristics and had Mayan people living in some parts of it. Sites in Soconusco such as Izapa represent a confusing mix of Mixe-Zoquean and Mayan architectural and cultural traditions, which is clear in their writing, which combined Mayan glyphic communication with more iconographic communication. Izapan writing "shared innovative formal traits and combinatorial conventions with the Southeastern tradition (Epi-Olmec, Kaminaljuyu, Tak'alik Ab'aj, lowland Mayan)...Izapa could have served as a meeting point for Mixean and Mayan speakers, and perhaps an interlingual use of writing was favored" (Mora-Marín 2018). The Aztec emperor conquered this area in 1486. This was one of the corners of the Aztec empire farthest from Tenochtitlan. We know little about its role aside from the fact that the Aztec collected tribute from at least eight towns in the region(the largest of which was known as Xoconusco), and that it was well known for its cacao production (Rosenswig 2008). So the only (partially) Mayan area conquered by the Aztec probably did not have a significant role in the empire outside of tribute payments.

Outside of Soconusco, we have few examples of contact between the Aztec and Mayan peoples. The groups knew about each other - relationships between the Maya and Central Mexican peoples are older than the Aztecs, as evidenced by the complex relationship between Tula and Chichen Itza. And trade routes in Mesoamerica stretched across the region, bringing resources between Aztec areas and Mayan ones. But as a rule, these trade routes were probably made up of itinerant traders present in both Aztec and Mayan society, or states relaying goods between each other in processes that linked far-apart regions without that direct goal. Trade routes like this would have operated somewhat like the Eurasian Silk Road in the sense that goods moved across them propelled by economic forces and did not require the organization of any single civilization, or pair of civilizations. In this system, Aztec and Mayan peoples could have been trading with one another without even realizing it.

For all their differences, the Maya and Aztec shared cultural similarities that result from the shared history of Mesoamerican civilizations. One of the best examples of this was the feathered serpent deity known as Kukulkan by the Yucatec Maya and Quetzalcoatl by the Aztec. This similarity among others is not a result of a direct relationship between the Aztec and Maya, but instead a continuation of millennia of consistent interaction and cultural diffusion across the region that they shared.

So, in short, modern knowledge suggests the Maya and Aztec did not have much direct contact with one another in the pre-Hispanic period. The only major place where this would have occurred was in Soconusco, where the Aztec conquered and pulled tribute from Mayan and Mayan-related peoples.

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Coggins, C. (1996). Creation Religion and the Numbers at Teotihuacan and Izapa. RES: Anthropology and Aesthetics, (29/30), 16-38.

Kappelman, J. (2004). Demystifying the Late Preclassic Izapan-Style Stela-Altar "Cult". RES: Anthropology and Aesthetics, (45), 99-122.

Mora-Marín, D.,F. (2018). Izapan Writing: Classification and Preliminary Observations. Ancient Mesoamerica, 29(1), 93-112.

Rosenswig, R. (2008). Prehispanic Settlement in the Cuauhtémoc Region of the Soconusco, Chiapas, Mexico. Journal of Field Archaeology, 33(4), 389-411.

I’m going to cheat your premise a little and talk about the Huastecs, a Mayan speaking people in northeastern Mexico, including parts of modern San Luis Potosí, Veracruz, Tamaulipas, and likely Puebla, Guanajuato, Hidalgo, and Querétaro, far outside of the traditional area of Southern Mexico, Guatemala, and Belize. This language group seems to be one of the first to split away from Proto-Mayan, and are thought to represent an early migration (early Formative or late Archaic periods, perhaps around 2000 BCE) northwards that was cut off by the later coastal expansion of Mixe-Zoque (thought to be the Olmecs) and later Totonac speakers along the Gulf Coast.

The Huastecs never achieved the sort of cultural hegemony in the area similar to the Totonacs, although they flourished briefly between the fall of Classic period center of El Tajín (~1200CE) and the rise of late Postclassic Cempoala (~1400CE). Several Huastec towns were conquered by the Aztecs under the reign of Motecuhzoma I around 1450, as the tropical lowlands were prized for agricultural products that weren’t able to be grown at the higher elevations of the Valley of Mexico - chiefly cotton and vanilla in this region. Speaking a Mayan language and living on the coast made them well positioned to trade up and down the Gulf, and the connections between Mesoamerica and Mississippian civilization that have been attested through shared cosmology, architectural plans, and import of Caribbean marine products has been frequently keyed to this region.

Per Archaeologist Richard Diehl (http://www.famsi.org/research/diehl/section01g.html) “the Huastecs suffered two very serious defects in the eyes of the rather puritanical Aztecs. The men generally did not wear loincloths, preferring to leave their genitals exposed, a practice that scandalized Aztecs and Spaniards alike. Furthermore, they loved pulque, an intoxicating drink made by fermenting sap from the maguey or agave cactus, in what the Aztecs considered excessive quantities.” The Aztecs considered the Huastecs to be filthy and barely civilized, but for those same reasons powerfully fertile. Huastec captives or dancers in Huastec costumes accompanied the processions of agricultural deities, and the Aztec goddess Tlazolteotl, mother of filth, lust, renewal from putrescence (sometimes depicted as coprophagia!), and penitence from sin is closely identified with them (or may even have been an importation from the region). The spiral cut conch shell that Quetzalcoatl/Ehecatl wears around his neck is also seen as a Huastec symbol, although this may indicate the directionality of the wind during the planting season.

To return to the question, the relationship between this Maya group and the Aztecs was one of colonial subordination of an exotic people, rhetorically useful both as a moral contrast to upright behavior and as a source of powerful but chaotic energy. Because most of our information is filtered through Nahuatl interpretation, it’s hard to get a picture of what the Huastecs thought about themselves or in turn the Aztecs - there are several tens of thousands of native speakers left in northern Veracruz and San Luis Potosí, but I do not know the ethnography or sociology of the region very well.

Delgado de Cantu, Gloria M. (1977) La Huasteca. Cultura-origen en Mesoamérica y punto de enlace con el sureste de Estados Unidos. Reuniones de Mesa Redonda (15 session). v. 1. pp. 439-446. Mesa Redonda, 15 , Sociedad Mexicana de Antropología

Diehl, Richard A. (2000) Precolumbian cultures of the Gulf Coast. Mesoamerica, pt. 1. R. E. W. Adams and M. J. MacLeod, eds. pp. 156-196. Cambridge History of the Native Peoples of the America, 2 . Cambridge University Press

Kehoe, Alice (2005) Wind Jewels and Paddling Gods: The Mississippian Southeast in the Postclassic Mesoamerican World. In Gulf Coast Archaeology, the Southeastern United States and Mexico, ed. Nancy Marie White. Gainesville: University Press of Florida. Pp. 260-280

Sahagún, Bernardino de (1950–82) [ca. 1540–85]. Florentine Codex: General History of the Things of New Spain, 13 vols. in 12. vols. I-XII. Charles E. Dibble and Arthur J.O. Anderson (eds., trans., notes and illus.) . Santa Fe, NM and Salt Lake City: School of American Research and the University of Utah Press.