Incorporated vs Unincorporated
Businesses may be run either in incorporated or unincorporated form.

Unincorporated businesses require very few steps (in some cases, none) to set up and take effect under the law. By contrast, an incorporated business must undergo a formal incorporation and registration process before it can legally exist.
Separate Legal Identity
From a legal perspective, an unincorporated business is usually treated as being the same as its owners, with no separate legal status. The most common forms of unincorporated business in the UK are the sole proprietor and partnership.
By contrast, incorporated businesses are legal entities which have a separate legal existence from that of their owners (also referred to as the shareholders). The most common forms of incorporated business in the UK are the private limited company and the limited liability partnership.