A project is a specific plan which one or more agents or teams intentionally supports during a specific period.
This intentionally expansive definition includes all organizations, companies and corporations. It includes solitary as well as collaborative projects, and all subprojects at all levels of design. Projects are often defined by the intention to create a specific product. Projects often require significant research and development.
Projects are created by persons, and are usually officially supported by one or more agents. (An unsupported project is often forgotten.) Projects may be sovereignly governed or governed by other people or projects. (Projects which are governed by other projects are subprojects). Each project has an identifiable mission, but that mission can (with due permission) be changed, and can lead to unexpected results.
Projects, or their stewards, often govern systems, but that happens with highly variable degrees of officiality and consistency. Project-based systems are sometimes highly elaborate, as with massive production systems and companies. Note that the supporters of "a project" don't necessarily support related system. (This is a common source of misunderstanding, confusion, stress and conflict.)
Many projects are collectives which are often defined by constitutional policies, and support many other policies.