A huarache sandal, technically, is a Mexican sandal with a woven leather strap upper.
That has changed a little bit because of the popularity of this book, Born to Run, about the Tarahumara Indians of Mexico who wear sandals for running. Their huaraches are a thong-style sandal made with a tire tread for the bottom and a leather upper on the foot bed and leather lace.
When Americans went down to the Copper Canyon in Mexico down and met the Tarahumara and they heard about these huaraches, they thought a huarache was the running sandal worn by the Tarahumara.
Once Born to Run got popular, that’s how many Americans began to think of a huarache as a running sandal, whether it’s a big thick one that looks like what’s to the left below or something from Xero Shoes that’s a modern version of the Tarahumara huarache that’s below to the right.