[Aztlan] Maya or Mayan?

[D. Cobb]

Introduced to the listgroup by my Hilis Heyv, I've been an on and off 
lurker for several years and enjoy reading the variety of topics. I am 
Maskoki, an archaeozoologist and caver and am fascinated by the 
similarities in the Maya and Creek beliefs, art, astronomy, and caves/ 
portals.
I've come out of hiding due to a wee pet peeve I've developed and hope 
y'all can clarify for me once and for all?
During a conversation on Creek & Maya cosmogeny, my dear friend, Andrew 
Weeks, corrected me by stating the word "Maya" references the people or 
culture, and the term "Mayan" is used only when referencing the language 
of the "Maya" people. It appears the Maya don't particularly like being 
called Mayan! Yet, hardly a day passes without hearing or reading Maya 
and Mayan used as if they are interchangeable? What gives?
It may seem silly to ask, but I want to be respectful so, do the Maya 
people prefer to be called Maya or Mayan and do they speak Maya or Mayan?
Thanks for any clarification y'all might offer!
Donna
Alabama