I am working with a beginner writer to help typeset their book for self-publishing. They would like to include an appendix which would explain the pronunciation of the numerous proper nouns that they had invented. It is the later word which is in question: is it more appropriate to refer to them as 'made up' or 'invented'?
Neither. These are terrible options for titling a glossary appendix. Neither is anywhere in the neighbourhood of mainstream usage.
“Terrible” may sound harsh, but that’s my immediate reaction as a reader. As a writer, I can explain the reaction: They emphasize the author’s relationship to the words—the author made them up—but that kind of intrusion of the author is contrary to keeping your reader’s thoughts within a state of suspended disbelief where they’re more accepting of made-up words. The reader already knows most or all of those words are made up; they just want the meaning.
Title the appendix “Glossary” and be done with it.
If there’s a particular unified source of these new words within the fiction, you can incorporate that in the title to strengthen the in-fiction (as opposed to out-of-fiction) source relationship in the mind of the reader: “Glossary of Atevi Terms” or “Glossary of Shevek’s Math”.
Reading the comments rather than question, this section seems to have a different purpose than a glossary.
For an appendix of the author’s notes on invented language or terms, neither “invented” nor “made up” are great.
Be specific instead: what are these? Are they names of planets or people? Title it “Author’s Notes on the Names of People and Places”. “Notes on…” or “Author’s Note (on…)” is mainstream.
Make the intrusion explicit. Let the reader know they’re exiting the realm of the fiction and sitting down with the author personally. The title should tell the reader what to expect.
I don't think either is "more appropriate" in every situation.
"Invented" is somewhat formal. It suggests to me that the author is thinking about the story world. In contrast, "made up" sounds to me as if the author is playing there.
Tolkien invented the languages spoken in Middle Earth. Lewis Carroll made up the words for Jabberwocky.
Which your friend wants depends on how each fits the tone of the rest of the book.