What term represents a business model where the business and the owners have distinct legal identities?

The term that represents a business model where the business and the owners have distinct legal identities is "Incorporated business." When a business is incorporated, it becomes a separate legal entity from its owners. This means that the corporation can own property, enter contracts, and be liable for debts independently of its shareholders.

Incorporation provides limited liability to its owners, meaning that their personal assets are generally protected from business liabilities. This distinction is crucial as it allows the owners to engage in business activities without exposing their personal wealth to business risks.

Other business models, such as partnerships or limited liability companies (LLCs), may allow for varying degrees of separation between the owners and the business but do not offer the same robust legal structure as corporations. The term "corporation" is closely related but does not explicitly denote the element of distinct legal identity as clearly as "incorporated business."