Cooperative: Often referred to as a "co-op", a cooperative is a limited-liability business that can organize as for-profit or not-for-profit. A cooperative differs from a corporation in that it has members, not shareholders, and they share decision-making authority. Cooperatives are typically classified as either consumer cooperatives or worker cooperatives. Cooperatives are fundamental to the ideology of economic democracy.
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Many businesses are operated through a separate entity such as a corporation or a partnership (either formed with or without limited liability). Most legal jurisdictions allow people to organize such an entity by filing certain charter documents with the relevant Secretary of State or equivalent and complying with certain other ongoing obligations. The relationships and legal rights of shareholders, limited partners, or members are governed partly by the charter documents and partly by the law of the jurisdiction where the entity is organized. Generally speaking, shareholders in a corporation, limited partners in a limited partnership, and members in a limited liability company are shielded from personal liability for the debts and obligations of the entity, which is legally treated as a separate "person". This means that unless there is misconduct, the owner's own possessions are strongly protected in law if the business does not succeed.
In legal parlance, the owners of a company are normally referred to as the "members". In a company limited or unlimited by shares (formed or incorporated with a share capital), this will be the shareholders. In a company limited by guarantee, this will be the guarantors. Some offshore jurisdictions have created special forms of offshore company in a bid to attract business for their jurisdictions. Examples include "segregated portfolio companies" and restricted purpose companies.
Having a business name does not separate the business entity from the owner, which means that the owner of the business is responsible and liable for debts incurred by the business. If the business acquires debts, the creditors can go after the owner's personal possessions. A business structure does not allow for corporate tax rates. The proprietor is personally taxed on all income from the business.
Charter corporations: Before the passing of modern companies legislation, these were the only types of companies. Now they are relatively rare, except for very old companies that still survive (of which there are still many, particularly many British banks), or modern societies that fulfill a quasi-regulatory function (for example, the Bank of England is a corporation formed by a modern charter).