Actually looking into this, it seems like it depends on jurisdiction. What you are saying seems to be true in England and USA, but here in Sweden the definitions seems to exclude foundations, as they have neither members or owners, and therefore they are not a group of people.
A corporation is just a group of people authorised to act as a single legal entity. Charities, foundations, etc, are corporations. They're corporate.
Actually looking into this, it seems like it depends on jurisdiction. What you are saying seems to be true in England and USA, but here in Sweden the definitions seems to exclude foundations, as they have neither members or owners, and therefore they are not a group of people.