In the legal context, the owners of a company are normally referred to as the "members". In a more 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.
The definition of a parent company differs by jurisdiction, with the definition normally being defined by way of laws dealing with companies in that jurisdiction.