A luxury sports car is called a GT.See Maserati Granturismo for example.
These cars are 3 door vehicles,and they are ideal for covering long distances,combining high levels of luxury and comfort with driving pleasure.There are many luxury sports cars out there,like the Mercedes Benz CL,the Maserati Granturismo,the BMW 6 series,a Bentley Continental etc
During the past years,a new category of GT vehicles has evolved.It offers the same as conventional GT cars,but with added practicality.These cars have 4 doors but do not look like conventional saloon vehicles.They look rather more like a coupe car.This category includes the Mercedes Benz CLS,the Audi A7,the BMW 6 Series Grancoupe (isn't on the market yet),the Aston Martin Rapide etc
And finally,there are normal luxury cars,whose main focus is comfort,luxury,safety and high end technology.This category includes the likes of Mercedes Benz S Class,BMW 7 Series,Audi A8,Maserati Quattroporte,Porsche Panamera etc.Sportier ones are the BMW,Maserati and Porsche
I hope that helped