Private limited companies and public limited companies differ in ownership and operation. Private limited companies are owned by shareholders and run by directors, while public limited companies' shares can be traded on a stock exchange. Both company types must register with Companies House and produce legal documents like a Memorandum of Association. A private limited company has 1-99 shareholders and its shares cannot be publicly traded, while a public limited company can have an unlimited number of shareholders and trades shares on a stock exchange to raise capital. Both types of companies provide liability protection to shareholders but have different legal and reporting requirements.