The key difference between rubber and silicone is that the backbones of most of the rubber forms contain carbon-carbon bonds while the backbone of silicone contains silicon and oxygen.
Both rubber and silicone are elastomers. They are polymeric materials that exhibit the viscoelastic behaviour, which we generally call as elasticity. We can distinguish silicone from rubbers by the atomic structure. In addition, silicones have more special properties than normal rubbers. Rubbers are naturally occurring, or else we can synthesize them, but silicon is only synthetic in nature. Depending on these, we can find the difference between silicone and rubber.