How was the process in which the northwest territories became states different from how the thirteen colonies became state

Unlike the thirteen colonies which became states by the process of unifying each others governments to form one sovereign state, the northwestern territories states were a product of the westward expansion.

Events such as the Louisiana Purchase, the Gold Rush, the Oregon Trail  managed to expand the United States to the west and many territories were therefore either bought, adjudicated or won. These territories wanted to be represented and considered in congress which eventually led to these territories bidding to become states themselves and become part of the union.

conformal maps greatly distort _sizes_ of continents in higher latitudes.

the answer is sizes.