There are several types of business and the type you choose will depend on several factors including what the business is, what your personnel circumstances are and what you need.
Common types of business structure:
This is somebody trading on their own account. There is no difference between the owner and the business and if necessary you have unlimited liability to pay those debts from your assets.
This is similar to a sole trader except that this is where there are 2 or more people in business together sharing the profits.
This is where a new legal entity is created or "incorporated" at companies house. This company then trades on behalf of the shareholders. The company is separate from the shareholders and directors and pays corporation tax based upon its profits. The shareholders liability is limited (hence the name) to the share capital they have agreed to buy. There are other "Business Structures" contact me if you wish to discuss and start up your business.