What is the difference between a public limited company and a public sector?

What is the difference between a public limited company and a public sector?
A public limited company is a corporate entity that openly sells its shares on the stock exchange and has share holders ranging from one to infinity (1-infinity).Its headed by officials who are elected every end of the financial year at the Annual General Meeting. Public sector accounting is applied. Examples include General Motors, Toyota etc while public sector is is used to refer to government owned corporate entities (in most cases the government is the biggest share holders here) and the shares are not sold on the stock exchange.