It appears that Nathaniel W. Smith may have served in both the militia and the regular army during the War of 1812. The National Archives has the service record of a Nathaniel Smith who was a sergeant in Colonel John Williams’ Mounted Volunteer Regiment of East Tennessee. His service record is located in roll box 193, roll record 9755.
The Tennessee Archives has a history of this regiment on-line:
COLONEL JOHN WILLIAMS DESIGNATION: Mounted Volunteers of East Tennessee DATES: December 1812 - March 1813 MEN MOSTLY FROM: Blount, Grainger, Knox, and Washington Counties CAPTAINS: Samuel Bunch, David Vance, William Walker BRIEF HISTORY: While the volunteers under Andrew Jackson were gathering at Nashville for their expedition to the Natchez region, a similar gathering was taking place in Knoxville. Their destination was the territory of East Florida, under the domain of Spain, and the leader of the expedition was John Williams of Knox County. Williams, along with approximately 250 volunteers, marched to East Florida to join with the combined forces of U.S. troops and Georgia "patriots" to "liberate" this region from Spanish control. Ostensibly, the expedition was raised to eliminate the threat of marauding Creeks and Seminoles on the borders of Georgia. Like Jackson's Natchez Expedition, the men of the Florida Expedition were considered to be from the finest families of the region and, like the Natchez Expedition, the excursion into Florida accomplished little. Some Creek villages were destroyed and the Tennessee volunteers suffered only one casualty. John Williams later became colonel of the 39th U.S. Infantry, a unit instrumental in Jackson's victory at Horseshoe Bend (27 March 1814).
If he served with Sam Houston then he was also in the 39th Regiment of U.S. Infantry, U.S. Army. Sam Houston was a 2nd Lieutenant in the 39th Infantry. On 17 May 1815 the regiment merged with other army regiments to form the new 1st Regiment of U.S. Infantry. This regiment served in the Seminole Wars.
Although the militia did not keep any genealogical information on its militiamen, the U.S. Army did. You could get the information that you are looking for and maybe more from Smith’s army records. On NAFT Form 86 (Military Service Records) from the National Archives mark “regular” for army service in Box 6 (Kind of Service).
The National Archives has the consolidated enlistment rosters for all of the U.S. Army regiments that served during the war in book form. This book is called the Records of the Men Enlisted in the U.S. Army Prior to the Peace Establishment, May 17, 1815. This book contains the name and rank of each enlisted personnel, his regiment, his company commander’s name, his regimental commander’s name, a physical description of your ancestor plus his peacetime occupation, where he was born (county and state, or country), where he enlisted and the period of enlistment, and any additional remarks. All of the columns may not be filled in. A page from this book will be sent to you as your ancestor’s service record.
Eric E. Johnson General Society of the War of 1812