A limited company is a formal legal entity created through incorporation under the Companies Act. When you incorporate a company, the Registrar issues a Certificate of Incorporation [Companies Act, S.10], giving your business separate legal status. This means the company itself owns property, enters contracts, and can sue or be sued independently from its owners. A private company limited by shares can have up to 50 shareholders and they have limited liability, meaning they are only responsible for debts up to the amount they invested [Companies Act, S.2].
A registered business name, by contrast, is simply a name under which you operate a business [Companies Act, S.1]. It is not a separate legal entity. If you operate under a registered business name, you personally (as an individual or partnership) own the business and are fully liable for all debts and obligations. There is no incorporation process and no limited liability protection.
The key practical differences are: a limited company has a separate legal personality and provides liability protection to its owners; a registered business name does not. A company requires formal registration and ongoing compliance; a business name requires simpler registration of the trading name you use. If you want to build a business with limited personal risk and create an asset that can be bought or sold separately from yourself, you should incorporate as a company. If you want to operate informally under a business name, registration as a business name may suit you, but you bear all the business risk personally.