I have been trying to find recorded instances of contact between the civilizations of the Aztecs and the Mayans. What I have found is reasons given for why they did not have contact. Basically, the zenith of Mayan civilization was much earlier than that of the Aztecs. I would guess, based on this, that while the Mayans were near their peak the Aztecs were only beginning to leave the jungle or where-ever they came from. So this the reason for no contact. The Aztecs were in mainly what is now Mexico and the Mayans were in what is now Guatamala and Belize. The Aztecs spoke Nahuatl and the Mayans spoke Mayan. I had assumed that the Mayans spoke Quechua, but I find that Quechua was the language of the Inca Empire. The point of this is that I think there should have been some contact. If the Mayans were at a higher level of civilization they could have gone on raids to enslave Aztecs. There was plenty of that kind of warfare going on. Both cultures engaged in ritual warfare and human sacrifice. Both built pyramids or pyramid-like structures. It is harder to find examples of Aztec writing. I have found only a small amount of Aztec glyphs. Maybe the Aztecs suffered more wholesale destruction of their documents by the conquistadors than did the Mayans. Well, I have alot to learn about Central American history. This quest will continue.

The language of the Incas is Quechua, the language of the Aztecs is Nahuatl, the language of the Mayans is Maya (or "Quiche Maya" to be exact). The following are the language branches descended from Quiche Maya:

Wastek branch
Yucatek Mayan branch
Ch'olan branch
Tzeltalan branch
Q'anjobalan branch
Quichean-Mamean branch
Mamean branch
Poqom branch

But why would they have mounted an expedition hundreds of miles to the north and west (on foot, mind you, since they had no horses) through inhospitable deserts and tremendous mountain ranges, when there were already thousands of potential slaves within easy reach? Did the Etrurians go looking for slaves in Bavaria? Did the Hittites raid the ancient Kartvelian state of Iberia?

As for the commonalities, ideas can diffuse without direct contact. Did it take Greek-speaking Jews to convert Scandinavia to Christianity? Was it Anatolian peasants who taught the ancient Britons to plant wheat? Both the Aztecs and the Maya drew from previous civilisations which had flourished in the area. The Olmecs, in particular, are considered responsible for originating many distinctly Mesoamerican cultural traits, among them the sort of ritual sacrifice you mention, as well as writing, the 260-day ritual calendar, and the ballgame ulama (called ullamaliztli by the Aztec and pitz by the Maya).

Keep in mind that the Mayan and Aztecs empires were just that, empires. What we think of as the Maya were actually many villages, who were autonomous (must like Greek city states) before they were conquered/joined the empire. For this reason they may be referred to by their local names.

Also, if you want to look for contact between the two civilizations, look at archaeological sources. Many times casual contact or trade does not survive in the written record. This is at least true for monumental carvings. As far as I know that is how writing was used in Mayan and Aztec civilizations.