The historical Aztecs and Maya were different groups of people. The Maya lived on and around the Yucatan Peninsula, while the Aztec were centered on central Mexico. The two groups shared some similarities - like feathered serpent deities - because they were part of the culturally related Mesoamerican civilizations, but spoke different languages, amongst many other unrelated characteristics.

It gets a little more confusing because the Maya weren't really a single unified empire or civilization themselves, at any point in history. Saying "the Maya" is a little similar to saying "Europe": both groups are/were closely knit systems of independent states which regularly competed with each other. Maya people spoke different languages from other Maya people (there are still many different Maya languages spoken today), even though those languages were related.

The aspect of Apocalypto's timeline that you're wondering out still makes sense, since the Maya civilization actually did not end in the 10th century A.D. What you're referring to is known as the "Classic Maya Collapse," which was certainly a period of intense change, cultural upheaval, and regional population loss. However, Maya civilization definitely continued after the "collapse," and continued to create large, politically complex systems like League of Mayapan. In fact, the last independent Maya kingdom fell in 1697, and many Maya groups have remained largely autonomous to the current day.

So (even though there are many other problems with the movie) Apocalypto is correct in portraying Europeans contacting Maya people in the 1500s.