Here’s the difference:
1) A sole proprietor is an individual that carries on a business. If things go wrong and his/her assets are on the line along with assets that he/she owns jointly with someone else, for example, the family home. Common sole proprietors are small businesses such as a plumber and local butcher shop.
2) A partnership is where 2 or more entities combine and carry on a business. Common partnerships are that in accounting or law firms. Where someone may become a partner.
3) A company is a legal entity which mean it can enter into transactions and incur debts by itself. The main benefit of having a company structure is that your personal assets aren’t at risk (unless the courts find you liable as a director). It also involves more expense (accounting, legal expenses). This structure is very common, think about large companies and most likely they will be a company structure.
Next: What is Accounts Payable... and What's Accounts Receivable?