The barefoot movement has prompted some manufacturers to introduce minimalist shoes, thin-soled and flexible shoes such as traditional moccasins and huaraches for minimalist running.

It does sound weird, but barefoot running is more broadly associated with any type of running that includes 0-drop heels and thin-soled “minimalist” shoes of various types. Can say minimalist running, but they’re often used interchangeably. In fairness I do like raw doggin’ it occasionally, too.