Burritos are a dish original from northern Mexico. A variation of the original burrito has become very popular as a Tex-Mex dish. One thing has been preserved from the original burrito: the fact that they are prepared with wheat tortillas (not the corn tortilla used widely in Mexican cousine).
It is impossible to have a unified version of a Burrito recipe. Almost any "rolled taco" made with wheat tortillas would qualify as far as it has something more than cheese inside. As said before, the burrito must be rolled otherwise it would be a "Taco".
Mexicans do not add rice, sour cream or lettuce to their burritos. Beans might be present but in a "spread" version -frijoles refritos.