In chemistry terms the difference between polymeric and silicone

is that polymeric is of, relating to, or consisting of a polymer. Examples of such compounds include polyurethane foams, PVC foams, and styrofoam while silicone is any of a class of inert, semi-inorganic polymeric compounds (polysiloxanes), that have a wide range of thermal stability and extreme water repellence, used in a very wide range of industrial applications, and in prosthetic replacements for body parts.

As an adjective polymeric

is of, relating to, or consisting of a polymer. Examples of such compounds include polyurethane foams, PVC foams, and styrofoam.

As a noun silicone is

any of a class of inert, semi-inorganic polymeric compounds (polysiloxanes), that have a wide range of thermal stability and extreme water repellence, used in a very wide range of industrial applications, and in prosthetic replacements for body parts.