clj command is for the Clojure CLI which is a different tool to
lein and therefore a separate install.
Leiningen projects use a
project.clj file to describe dependencies, plugins, etc.
Clojure CLI projects use a
deps.edn file to describe dependencies etc.
They are two different ways to work with Clojure.
"Clojure" itself is really just libraries that you use as dependencies in projects -- you don't really "install" it. Since Clojure 1.9 there is no single JAR file you can download and use -- you must use Clojure as a dependency -- so you need to use some tooling that handles dependency management for you: either Leiningen or the Clojure CLI (or Boot, but you're not asking about that).