Question

Do You Know:

There is one more form of plastics known as Elastomers. This is a small group of polymers, which can be stretched and deformed at room temperature. Elastic and rubber are examples of elastomers.

does this mean that rubber is synthetic ?

Answer 1

An elastomer for the purpose of this classification is a rubber-like material capable of vulcanization, such as copolymers of butadiene and styrene, or butadiene and acrylonitrile, polybutadienes, chloroprene rubbers, and isobutylene-isoprene copolymers.

Synthetic Rubber is known as Vulcanizable Elastomers.

In Broad sense all rubbers which can be vulcanized whether natural or synthetic rubber as classified as elastomer. You're thinking in right direction.