BBC Studios produced the British television version of Dragon’s Den for the BBC.
The programme belongs to the BBC’s wider family of factual-entertainment and format productions. Its production history is sometimes described using older BBC corporate names because the organisation has changed structure and branding over time.
BBC Studios is the BBC’s commercial production and distribution arm. It creates programmes for the BBC and other broadcasters, and it also manages international format and distribution activity. Dragon’s Den sits within that broader television-business operation.
This question is about the production company, not the broadcaster. BBC Two was the original UK channel for the programme, while BBC Studios refers to the organisation involved in making and commercially handling BBC content. Those roles are related but not interchangeable.