> A company town is a place where practically all stores and housing are owned by the one company that is also the main employer.

I'm not familiar with varying types, but AFAIU (or hope), the organizer / owner is not usually the main employer. It's foremost a community where people live. Some people work there or self-employ, but it's not usually a corporate-dictated, top-down governed establishment, which would be something quite different. At least in the examples I know of.

Not if it's organized as a corporation where all of the residents are voting shareholders. That's generally the model that most cohousing and intentional communities tend towards.