"The Diccionario de Mexicanismos has an entry for the burrito as early as 1895" ... "The entry states that a burrito is 'A rolled tortilla with meat or other ingredients inside, called ‘coçito’ in Yucatán and ‘taco’ in the city of Cuernavaca and in Mexico City.'”
So, how I understand this is that, what people in a certain region back then referred to as a burrito, was just the humble taco that we know and love today.
The burrito as we know it, isn't from Mexico.
Although, one could argue that a burrito is simply a taco with the ends tucked in.