Because, like so many things, there is a difference between the company name and the brand : cf NatWest, ASDA, TFL etc.
I know that, there is a difference though. Natwest and Asda are wholey owned subsidiaries of multi-national companies. BSkyB and Sky are one and the same
According to Wiki, Sky is British Sky Broadcasting Ltd, a subsidiary of BSkyB PLC.
Subsidiaries of BSkyB PLC are:-
British Sky Broadcasting Ltd
Operating company for the Sky pay-television service.
Sky Subscriber Services Ltd
The original Sky Television plc, now a holding company
Sports Internet Group Ltd
Sports content and online betting services.
British Interactive Broadcasting Holdings Ltd
Interactive television services, formerly an alliance of BSkyB, BT Group, HSBC and ****.
Mykindaplace.com
Being both an agency and a media owner, run many successful sites. – Now defunct
Aura Sports Ltd
Media Sales Agency, sells advertising on the majority of premiership football club websites, as well as other major sports.
Aura Play Ltd
Another Media Sales Agency, sells advertising across a number of websites in the music and entertainment sector.
Sky Ireland
Operating company for Sky pay-television service in the Republic of Ireland.
Living TV Group
A British television content arm, operating a number of channels.