What type of American territory or region is similar to a province?

A state, A province is almost always in administrative division within a country or state

When a portion of the Missouri Territory became the state of Missouri, the remainder of the territory (the present-day states of Iowa, Nebraska, South Dakota and North Dakota, most of Kansas, Wyoming, and Montana, and parts of Colorado and Minnesota) became an unorganized territory.

Area: 22,294.19 km² (8,607.83 sq mi)

Languages: English, Spanish, Chamorro, Carolinian, Samoan

Currency: United States dollar

Largest settlement: San Juan, Puerto Rico