Have you noticed bikes labeled "Audax bike"?
These are bicycles which the manufacturer consider ideally suited for riding long distances at faster than a leisurely pace. They are not 'Road bikes'. They are what were formerly known as 'sports tourers'. Marketing hype has renamed them to appeal to the ignorant.
A 'sports' bike, as has been said before, is a lower cost heavier version of a 'Roadbike'.
The term "Racer" was banded about because when and if cycling apeared on the newsreel, these were the cyclist who were shown. The public associated dropped bars and no mudguards with the Racing chappies on the moving pictures Pathe news before the main feature.
There were of course 'Tourers', which were not always equiped with derailleur gears, they were usually Sturmey Archer with small chainrings and larger than 20 tooth sprockets, racks, panniers, mudguards and a cyclimeter. Most had semi-dropped bars for comfort and the general public saw the semi-drops and incorrectly thought "Racer".