In Mexico, it is only called dulce de leche if it is made with cow's milk. The same sweet has a different name if the milk comes from a goat. Other name variations are simply regional and have little to do with how the sweet is made.
In fact, many foods have different names here in Chile, than in other Spanish-speaking countries. For example, corn (normally called maíz or elote) is choclo here. Mushrooms (champiñones, setas, or hongos) are sometimes called callampas here. This makes ordering food in a Chilean restaurant an adventure every time!
