You're right, my mistake. I was thinking of Existential Nihilism which is a school of thought within Nihilism, but is different in it's interpretation as I described in my original post.

Existential nihilism is the philosophical theory that life has no objective meaning or purpose... The inherent meaninglessness of life is largely explored in the philosophical school of existentialism, where one can potentially create their own subjective "meaning" or "purpose".

... Friedrich Nietzsche further expanded on these ideas, and ... has become a major figure in existential nihilism.

There are also some quotes of note in the main Nihilism Wikipedia article

Nietzsche distinguishes a morality that is strong or healthy, meaning that the person in question is aware that he constructs it himself, from weak morality, where the interpretation is projected on to something external.

As such, the self-dissolution of Christianity constitutes yet another form of nihilism. Because Christianity was an interpretation that posited itself as the interpretation, Nietzsche states that this dissolution leads beyond skepticism to a distrust of all meaning.

I think Absurdism is more what people are generally describing when they use the term Nihilism in popular culture. Here are a couple of excerpts from the same Existential Nihilism Wikipedia article I linked.

The supposed conflict between our desire for meaning and the reality of a meaningless world is explored in the philosophical school of absurdism.

With Kierkegaard, the concept of absurdism was developed, which explains the concept of humans trying to find meaning in a meaningless world.