Most tires are not made from natural rubber, but from synthetics.

Yet, it is still not literally a plastic by definition. I feel the term “plastic” is already demonized enough, and now it often serves as a generic umbrella term for alarmist purposes.

How are you defining plastic that synthetic tires don't fit the definition?

Plastics are rigid, while rubber (elastomers) is elastic.

You might say this is nitpicking, but not everything that's potentially harmful in its dispersed form is plastic. Asbestos, coal dust, and sand dust are not plastics.

For me, it's like calling any shiny metal 'silver' or calling any clear stone a 'diamond' - they may look similar, but they're completely different materials.

Ah. Got it. You're talking about rigid plastics. Not all plastics are rigid. Polyester and nylon are frequently spun into thin fibers so they are flexible for clothing, and plastic bags are a thing. Plastic lids are frequently flexible so you can actually put them in the container. Rigid plastics are not the only kind that exist.