Sound Transmission Class (STC) is a rating of how well a building partition attenuates airborne sound (eg. TV or radio). STC is dominated by the mass in an assembly (e.g. Concrete vs. wood construction). This number is minimally affected by the floor covering and/or underlayment.
Impact Insulation Class (IIC) is a rating of how well a floor-ceiling assembly attenuates impact sounds (footsteps, dropped items). IIC is dominated by material properties and installation methods. This number can be significantly improved by the proper floor covering and underlayment.