More specifically how did these groups refer to their own architecture in their native languages? Are there any primary sources suspect, as many new world documents can be, or not that reference how these or later groups referred to their architecture?
I highly recommend reading The Code of Kings: The Language of Seven Sacred Temples and Tombs by Linda Schele and Peter Mathews. Together these Maya researchers break down the symbolism and meaning found in Classic Maya structures from around the region. It is highly informative and combines epigraphy and archaeology for a truly wonderful read.
That being said, to answer your question as it pertains to the Classic Maya, they refer to their pyramids in their texts as witz or "mountain". This is because the Maya conceived mountains as being living beings, both the home and representation of gods. Many of the pyramids would have had zoomorphic elements like eyes, mouths, ear ornaments, and muzzles done in stucco to give them the physical appearance of living beings.
The pyramids are tied to two cosmological pyramids, Sustenance Mountain and Snake Mountain. Sustenance Mountain refers to the cleft mountain in which the Maize God emerged and brought with him the knowledge of maize. Snake Mountain is a mountain monster in which snakes emerge from an opening in the mountain.
Pyramids are usually associated with some sort of cave and this cave is a representation of a path to the Underworld. In cases where there is no cave there is sometimes a witz monster decoration around a doorway which transforms the space within to a cave.
Public buildings are sometimes referred to as xanil nah, "thatch house", even if they are not necessarily made out of thatch. A typical house is called Otot.
Council houses have several names/terms. The most common I've seen is popol nah, "mat house*, but they could also be referred to as nikte'il nah, "flower house", or sak nah, "white house". Council houses are where nobles gathered sometimes for political function and sometimes for dancing and feasting. Council houses were also places in which ritual regalia for ceremonies was often kept.
Plazas are called ol and had a symbolic association with the Primordial Sea. To keep plazas from flooding and taking the metaphor too far, many of them had built in drainage systems to keep them free from standing water when it rained.
Roads connecting settlements are referred to as sakbe, "white road". There are raised earthen and plastered roads several meters wide that can run for kilometers between settlements. I've seen in the Puuc region that the beginnings of sakbe are marked with an arch, but this doesn't hold true to every Maya region.
This is a summary of some of the major features. Like I said, there is a whole book on the subject of Maya architecture and its symbolism if you are interested.