Okay, according to the source I have, Xoloitzcuintli is just another name for the Mexican Hairless, This breed was developed by the Aztecs, and can come on a "Powder puff" version, which does have hair, but they can't be show dogs.

The Chinese Crested was developed half a world away, in China, and was first seen in the Han dynasty. It, too has a "hairy" or "Powder puff" version, and these apparently CAN be show dogs! Even the "hairless" version of the Chinese Crested does have long fur on his head and ankles, unlike the Mexican Hairless. Oh, yeah, the Mexican Hairless comes in standard, miniature and toy sizes, the CC in just one.

Aren't books great?