People have been failing to understand philosophy since philosophy was invented.
Let’s see if I got it!
Nihilism: the general idea that nothing can truly be known, proven, or objective in any way.
Existentialism: the general idea that each person creates their own meaning for existence.
Existential Nihilism: the idea that each person creates their own meaning for existence, but it’s impossible to prove one meaning is objectively better or worse than another.
The definition you gave for nihilism sounds like epistemological nihilism (‘nothing can be known’), which is one type of nihilism. Existential nihilism (‘nothing has innate meaning’) is another type, moral nihilism (‘nothing is right or wrong’) yet another. One person can hold any combination of these views.