Plastic is tough. It's everything from the dashboard of a car to a child's toy. I'm writing this on a plastic keyboard. Plastics surely were the future. Polymerization is a plastics manufacturing method that involves materials with high molecular weights and semisynthetic organic compounds.
Polymers are the types of plastics created by polymerization.
Plastics can be molded, injected, cast, extruded, drawn or laminated under a variety of conditions. Heat is used to form thermoplastics. Casting is often used in polymerization to form objects of all sizes and shapes. A polymer is nothing more than a plastic that has been formed by polymerization. I don't mean to be polemical about all this, but a polymer is a plastic.