one is considered NCO and has more duties, while a specialist isn't (in most cases and MOSs)
Specialist (abbreviated "SPC") is one section of the fourth enlisted rank in the U.S. Army, just above Private First Class and below Corporal. It shares the same enlisted pay grade as the Corporal, which is a rank for non-commissioned officers (NCO).
In the U.S. Army a Corporal (CPL) is the fourth enlisted rank, the first three being forms of Private and the fourth being the Specialist. A Corporal ranks above a Specialist and below a Sergeant, and has the same pay grade (E-4) as a Specialist.
Unlike a Specialist, a Corporal is a non-commissioned officer and may direct the activities of other soldiers, including Specialists. Corporal is the most junior non-commissioned officer rank. A promotion from Specialist to Corporal is a lateral promotion: an increase in rank but not in pay grade. Currently, very few soldiers are made Corporal; most go from Private First Class to Specialist to Sergeant. However, Corporals are found in some combat units. The typical criteria for promotion to Corporal is that the Specialist must be serving in a leadership position which would typically be occupied by an NCO such as a Sergeant.
It is common for a Corporal to lead a fireteam; however, if a soldier is promoted to Corporal and there are too many soldiers of that rank, the new Corporal will stay in his current position.
The rank of Corporal is the only rank in the United States Army that has never been removed from the NCO Corps.