Chihuahuas originated in Mexico, but they are not a separate breed from those found elsewhere. The name "Chihuahua" comes from the Mexican state of Chihuahua, where the breed was first identified.
All Chihuahuas are considered the same breed, regardless of their origin or location. There may be subtle differences in appearance or temperament based on breeding lines, but these are not breed-specific variations.
So, when you hear "Mexican Chihuahua", it's likely just a way of emphasizing the breed's origin, not a distinct type.