Mexico's rivers carry names in both Spanish (río) and English (river), reflecting the country's complex linguistic history rather than any geographic or hydrologic distinction.
Río is the standard term throughout Mexico—Río Bravo, Río Lerma, Río Balsas. This reflects Mexico's Spanish colonial heritage and the language spoken by the vast majority of its people.
English "River" appears in specific contexts:
Río Grande / Río Bravo: The same river forms the Texas-Mexico border. Americans call it the Rio Grande; Mexicans call it Río Bravo del Norte—both meaning "Big River" / "Wild River."
Colorado River / Río Colorado: In northwestern Mexico, both names are used for the river that carved the Grand Canyon and once reached the Gulf of California.
There's no official policy. Names reflect local tradition, historical accidents, and practical communication needs. A river doesn't change its nature based on what we call it—but the names we use tell stories about the people who named it.