A limited liability company (LLC for short) is the United States-specific form of a private limited company. It is a business structure that can combine the pass-through taxation of a partnership or sole proprietorship with the limited liability of a corporation. An LLC is not a corporation under state law; it is a legal form of a company that provides limited liability to its owners in many jurisdictions.
In law, liable means "responsible or answerable in law; legally obligated". Legal liability concerns both civil law and criminal law and can arise from various areas of law, such as contracts, torts, taxes, or fines given by government agencies. The claimant is the one who seeks to establish, or prove, liability. Claimants can prove liability through a myriad of different theories, known as theories of liability. Which theories of liability are available in a given case depends on nature of the law in question.
In law, a legal person is any person or 'thing' (less ambiguously, any legal entity) that can do the things a human person is usually able to do in law – such as enter into contracts, sue and be sued, own property, and so on. The reason for the term "legal person" is that some legal persons are not people: companies and corporations are "persons" legally speaking (they can legally do most of the things an ordinary person can do), but they are not people in a literal sense (human beings).
A holding company is a company whose primary business is holding a controlling interest in the securities of other companies. A holding company usually does not produce goods or services itself. Its purpose is to own stock of other companies to form a corporate group. In some jurisdictions around the world, holding companies are called parent companies, which, besides holding stock in other companies, can conduct trade and other business activities themselves.
A public company is a company whose ownership is organized via shares of stock which are intended to be freely traded on a stock exchange or in over-the-counter markets. A public (publicly traded) company can be listed on a stock exchange (listed company), which facilitates the trade of shares, or not (unlisted public company). In some jurisdictions, public companies over a certain size must be listed on an exchange. In most cases, public companies are private enterprises in the private sector, and "public" emphasizes their reporting and trading on the public markets.