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A royal colony is a colony that is a colony ruled by appointed officials. In United States history, New York was a royal colony governed by a council and a royal governor appointed by the British Crown. An administrator that has the overall rule over a land. 
A proprietary colony is a colony that were granted to an individual or group of individuals by an administrator, the British Crown for US history, and were granted full rights to self-govern to develop and self-govern the colony themselves without the Administrator's rule. 
Colonial governments assumed one of three forms: charter, proprietary, or royal. ... Proprietary colonies were granted by the King to a proprietor or head of a proprietary family, who owned the colony by title and governed it as he saw fit.
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