Teams revolve around a strong leader who usually allocates tasks rather than specific roles or functions.
Individuals within the team expect direct access to and feedback from the leader. Thus teams tend to be more a grouping of individuals working independently towards a common objective.
Many private companies are family-run and owned and family members would fill most management positions. Thus, the most obvious team grouping in a typical private company would be family-oriented but even this would be fairly hierarchical in nature.