Rubber, plastic and fiber are polymeric compounds. Molecular weight is not the difference between them. Differences: Rubber, also known as elastomer, has high elasticity at room temperature. Other chemicals do not have this kind of character. Plastic does not have high elasticity at room temperature.
Both rubber and plastic can be classified into different types. Every different type has different functional group and characteries. This is not the difference between rubber and plastic. Some rubber and plastic have the same functional group and similiar characteries.
Polyurethane is a kind of material whose properties are between rubber and plastic. When its molecular chain is short, it has good elasticity and can be used as rubber, but it is usually hard. When the molecular chain is long, its performance is close to plastic material.