What type of business is a mixture of private personal ownership and aspects of a corporation that delegates liability status of the person from the business?

The type of business you are describing is a Limited Liability Company (LLC). An LLC combines elements of both personal ownership and corporate structure, allowing owners (called members) to enjoy limited liability protection, meaning their personal assets are generally protected from business debts and liabilities. This structure also offers flexibility in management and taxation, making it a popular choice for small business owners.