Business is the activity of making one's living or making money by producing or buying and selling products (such as goods and services). It is also "any activity or enterprise entered into for profit."
Having a business name does not separate the business entity from the owner, which means that the owner of the business is responsible and liable for debts incurred by the business. If the business acquires debts, the creditors can go after the owner's personal possessions. A business structure does not allow for corporate tax rates. The proprietor is personally taxed on all income from the business.
Corporations, in contrast with sole proprietors and partnerships, are a separate legal entity and provide limited liability for their owners/members, as well as being subject to corporate tax rates. A corporation is more complicated and expensive to set up, but offers more protection and benefits for the owners/members.