A grille is a set of blades. Its strength is direction: you can aim the air, deflect it away from a seating position, or throw it along a ceiling. Its weakness is mixing. A grille discharges a flat sheet that keeps its shape for a while, which is exactly what you want in a perimeter installation under a window, and exactly what you do not want over a desk.
A diffuser is a geometry problem solved in metal. Swirl vanes or radial cones force the air to spin as it leaves, which pulls room air into the stream and mixes it within a short distance. The result is lower velocity at head height and less noise for the same airflow. That is why diffusers own the ceiling in offices, hospitals and hotels.
The practical rule we give consultants: perimeter and sill, use a grille. Occupied ceiling zones, use a diffuser. Very tall or long spaces, neither. Use a jet nozzle and aim it, because at fifteen meters of height a diffuser has already spent its energy before it reaches anyone.