Dry heat cooking methods like roasting and grilling use high heat to cook meat quickly while moist heat methods like braising and stewing use lower heat and liquid to slowly cook tougher cuts. The appropriate cooking method depends on factors like the cut of meat and its fat content to achieve tenderness and develop flavor. Roasts are roasted dry while tougher stew meat is braised long and slow. Ground meat can be cooked with either dry or moist methods.