At one extreme, there is what is derisively called "badge engineering" where brands are differentiated by a small number of details such as brand badges. The opposite extreme is the use of large amounts of differing sheet metal to give the basic body distinctly different appearances for each brand used. A classic, successful instance of the latter was 1966-67 bodies on General Motors' E Platform.
The brands and models involved were the 1966 Buick Riviera, the 1966 Oldsmobile Toronado and the 1967 Cadillac Eldorado. All were large, sporty coupes. And they were made to look so different that casual observers were unlikely to realize that they shared a common platform. Half a century ago, GM was rich enough to be able to do such things.