All the Territories were part of the United States.
Michigan was originally settled at Detroit by the French and was part of New France until captured by the British in 1760. It remained in British hands as part of the Province of Quebec (and then briefly Upper Canada) until 1796 when in Jay's Treaty, the British ceded it to the United States. So whatever the designation after that - Northwest Territory, Indiana Territory, Michigan Territory - they were all part of the United States.