Yes Yes Yes! There's the distinction of "Natural Elements" and I've always suspected that it was a somewhat temporal distinction. While I believe that the Periodic Table is a Universal Truth, "Natural" vs "Man-Made" elements always struck me as a Earthly way of looking at things. Not bad, just not the whole truth.
I really love the Isotope Table. I seem to remember having a chemistry teacher that mentioned something about the table being wonky or secretive. Total hearsay.
I like the periodic table because I could verify it. Isotopes? Not so much...
I don't think there's anything wonky about that table, it's just often not in the curriculum in high school, and teachers don't want to "confuse" students with material outside of the curriculum. But for me it greatly simplified understanding isotopes and radioactive decay.
And why would you think you couldn't verify it? All of the isotopes in the table were observed in a lab somewhere.
It turns out it's even worse than that. Plutonium and other "non-natural" elements have been found naturally occurring on Earth [1]. All sorts are supposed to have existed historically at the Oklo natural nuclear reactor too [2]. Probably safer to call them transuranic elements.