There is no "north state of New Mexico"—New Mexico is a state, bordered to the north by Colorado. The confusion may stem from New Mexico's north-south orientation or its northern region's distinct character (the Sangre de Cristo Rockies, high desert mesas, and Pueblo communities).
The region north of Santa Fe—Taos, Los Alamos, the Española Valley—differs culturally and ecologically from the southern desert basins. Higher elevation, heavier winter snow, historic Hispanic villages, and Pueblo nations create a subregion often called "Norteño" New Mexico. But administratively, it's all one state: the Land of Enchantment, with Colorado as its northern neighbor.