A burrito is not a sandwich. I'd argue that a burrito is its own category, or that "wraps" in general are their own category, which the burrito itself belongs to.
I've thought a lot about this debate. To me, the heuristics of what makes a sandwich are thus:
-The outside is a yeasted bread. A roll cut in half (separated or not), OR at least two slices of bread, or one large piece of bread folded. Examples: A sub, a club sandwich, a gyro or other pita sandwich (I read that pitas and other "flatbreads" use yeast). Tortillas do not contain yeast, so wraps and such are out. Pizza does not come pre-folded, it's out.
-It is not sealed shut (Like a burrito or calzone is). There is at least one open side when construction is complete.
-You can reasonably eat it with your hands without making a huge mess. This part is a little subjective. Crumbs are normal. Eating eggs benedict or an open-faced "sandwich" from a diner with your hands would be a mess; they are not sandwiches, despite their names (But they are delicious).
-My most controversial thought: You only need to eat one of said item to consider it a meal. This is extremely subjective, but it's how I arbitrarily justify not calling a hot dog a sandwich. If I have one hot dog, I am still very hungry. A 12-foot party sub counts because it started life as one very long sandwich that was cut into pieces. You have a few pieces, you have eaten a sandwich, just not an entire one.
Examples of sandwiches:
-Subs / heroes / hoagies / grinders
-Paninis
-Hamburgers on a bun
-Gyros / kebab sandwiches
Examples of "not sandwiches":
-Burritos, tacos, quesadillas, and pretty much every Mexican American staple besides the cemita and the torta.
-Open-faced anything
-Sushi
-Pizza