At least in drag racing, it is a full body car that doesn't have a roof or windows (not a convertible - there is a difference). Some roadsters are modified from original cars - the roof and the support posts are removed, as are the windshield and back window. The door joints are usually sealed, and the window openings and most of the interior are covered with added body panels. Other roadsters are purpose-built racecars using aftermarket manufactured bodies. I've seen some unusual roadsters in racing, but the most unusual is a pair of Gremlins, raced by a husband and wife team.