A company is a business entity registered under the Companies Act, Chapter 50. It has a legal personality i.e. it has rights to own properties, has perpetual succession and can sue or be sued in its own name. It usually has the words 'Pte Ltd' or 'Ltd' as part of its name.
A sole-proprietorship is a business owned by one person or one company. There are no partners. The sole-proprietor has absolute say in the running of the business.
A partnership is a business firm formed by two to twenty partners. Once there are more than twenty partners, the partnership must be registered as a company under the Companies Act, Cap. 50.