The wrap is defined by containment rather than by any filling. A flexible flatbread, usually a soft wheat tortilla, is laid flat, loaded along one edge or across the centre, and rolled completely around its contents so the bread encloses the food on every side instead of stacking it between two rigid faces. Taken under its bare generic name, this is the format itself, stated without a regional filling attached. What makes it a thing worth naming is precisely the engineering: a sealed cylinder of bread lets a loose, mixed, often wet filling be carried and eaten one-handed while moving, which a sliced-bread sandwich cannot do without falling apart.
The craft is structural before it is anything else. Because a rolled wrap is a closed tube, the filling has to be dry enough not to blow the seam and arranged so the contents are spread evenly down the length, since a wet centre splits the wrap along its weakest line and a clumped one gives bites that are all bread at one end and all filling at the other. The dressing is calibrated to bind without soaking, and the bread is usually warmed briefly so it folds and rolls tight rather than cracking along the fold. The roll is then often pressed seam-down or griddled so it holds its shape, because an unsealed wrap unrolls in the hand and defeats its own reason for existing.
The variations are the entire high-street menu, since almost any filling can be put through the format. A spiced chicken or salad filling makes the everyday lunch wrap; a pitta turns the same idea into a pocket that relies on the bread's own wall; a flatbread carrying spit-roasted meat and a sauce becomes a kebab. Each deserves its own article rather than being crowded in here.