You’re right and this is also a bit of a pet peeve of mine. “Lisp” hasn’t described a single language for more than forty years, but people still talk about it as if it were one.
Emacs lisp and Clojure are about as similar as Java and Rust. The shared heritage is apparent but the experience of actually using them is wildly different.
Btw, if someone wants to try a lisp that is quite functional in the modern sense (though not pure), Clojure is a great choice.