Proprietor: someone who owns a business; he is the only owner.
A sole proprietor files a Schedule C tax return.

Partnership: business that is owned by two or more persons who pool their resources and share the resulting profits and losses.
A partnership would file a 1065 tax return.

Corporation: business whose articles of incorporation have been granted within the state of operations.
A corporation would file an 1120 tax return.

S-Corporation: corporation whose primary income is derived from providing services of some kind. This includes doctors, lawyers, business consultants, and others. The rules for a S-Corporation are different from those of a Corporation.
A S-Corporation would file an 1120S tax return.

Personal: individual account that is non-business related.
A personal account would file a 1040 tax return (personal income and expenses).