For millions of years, nature has basically been getting by with just a few elements from the periodic table. Carbon, calcium, oxygen, hydrogen, nitrogen, phosphorus, silicon, sulfur, magnesium and potassium are the building blocks of almost all life on our planet (tree trunks, leaves, hairs, teeth, etc). However, to build the world of humans—including cities, health care products, railways, airplanes and their engines, computers, smartphones, and more—many more chemical elements are needed.
All of these types of plastic you’re using as counterexamples are more distinct from each other than they are from biological polymers.
Plastics are a ridiculously diverse group of chemicals, not including naturally occurring polymers is anthropocentric and not always useful.
What, in your opinion, is the semantic difference between the words plastic and polymer?
What is your word of choice to distinguish between naturally occurring and lab-made polymers?
It depends on the context. Sometimes plastic is good for that, but in this case I don’t believe that it is.
Plastic is not a rigorous term. When discussing specific plastics it’s petty much always better to describe specifics, because plastics are too diverse of chemistry to do anything else.