The premise is incorrect: Texas does not have a "North Texas Coastal Plains" region.
The Gulf Coastal Plains extend across southern and southeastern Texas—from the Sabine River (LA border) to the Rio Grande—covering the Houston, Corpus Christi, and Brownsville areas. They are characterized by:
"North Texas" typically means the Dallas-Fort Worth Metroplex and surrounding counties. This area lies in the Grand Prairie and Cross Timbers ecoregions—rolling plains, limestone cuestas, post oak savannas. It is inland, 250+ miles from the Gulf.
If you're studying Texas regions, use the standard physiographic provinces: Gulf Coastal Plains, Central Lowlands, Great Plains, Basin & Range.