The Spanish word 'petate' comes from the Nahuatl (Aztec) word 'petlatl', which meant 'reed mat'. This is one of many words that Spanish borrowed from the indigenous languages of the Americas during the colonial period. The word maintained its basic meaning of a mat made from woven reeds or similar plant fibers, often used for sleeping, while simplifying its pronunciation to fit Spanish phonology by dropping the final 'l'.

Since 'petate' entered Spanish directly from Nahuatl, there aren't any simpler or more common Spanish words that share its etymology. It's a relatively unique word that reflects the cultural exchange between Spanish and indigenous American languages.

There aren't any common English words directly related to 'petate', as it comes from Nahuatl. However, English has borrowed this word in some contexts, particularly in discussions of Latin American culture, where a 'petate' refers to the same kind of traditional sleeping mat.