Perhaps, but if we had come up with a new word, you or someone else would complain that we had done that instead of using a word that people already "understood". :-)
English is a language full of elision, and there's nothing inherently wrong with using one word for closely related meanings. When being precise, Rust uses the term "memory unsafety", but we humans usually shorten that to just "unsafety" because we are lazy.
My point was merely to state that a function throwing an exception [1] doesn't introduce memory unsafety.
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[1] Notably, we call this "panicking" in Rust-speak; does the fact that we call it something different from "exceptions" confuse people? Probably at least one.