Luxury sedans generally put four-door access and passenger comfort at the center of the design. Traditional coupes use two doors and a more enclosed rear-seat layout, often emphasizing their roofline and the experience of the front occupants. The most useful difference is how each body works for the people and belongings you carry.
The categories overlap. A coupe can be luxurious, and a sedan can be fast and engaging to drive. Some manufacturers also use coupe for four-door vehicles with sloping roofs. Look at the actual doors, seats, roof clearance, and luggage opening before drawing conclusions from the name.