Gyros Moskhári (Γύρος Μοσχάρι) is the beef reading of the spit, and the first thing to know is that it is the uncommon one: in Greece, pork and chicken dominate the cones, and beef is a comparatively rare order. That scarcity is the angle. When a counter runs a moskhári spit at all, it is making a deliberate choice, and the wrap is defined by how beef behaves differently from the meats it stands in for.
Beef is leaner and firmer than pork and carries a deeper, more mineral flavor than chicken, so the stack and the shave matter in a particular way. The meat is seasoned and layered onto the vertical cone, and as the outer face cooks the cook shaves it in ribbons; with beef those ribbons want a genuinely crisp, well-caramelized edge, because lean beef pulled pale and underdone from the interior turns chewy and flat fast. A good moskhári has that browned, slightly charred edge carrying most of the flavor. A weak one is grey, tough, and tastes of little, the lean meat punished by a cone that never built a proper crust.
The wrap around it is standard but recalibrated for the meat. Warmed soft bread, tzatziki to the edges, the hot shaved beef, tomato, onion, fries, rolled tight. Because beef brings less fat than pork, the tzatziki and the crisp edge do more of the work of keeping it from reading dry, and a good counter shaves the beef to order so it does not sit and stiffen. Restraint in the supporting cast lets the distinctly beefy note come through rather than be buried.
This stands apart from the more common cones. The chicken kotopoulo and the mixed miktós each lead from different meat entirely, and each deserves its own article rather than being crowded in here. What defines moskhári is the meat that is rarely on the spit: leaner, deeper-flavored beef that lives or dies on a properly crisped, freshly shaved edge.