Can someone explain all the differences in the various lisp modes (inferior, superior, slime, cider)? Which came first? Which are extra packages? What should one use?
When you run a process inside Emacs, that process is "inferior" (i.e. a subprocess).
IELM M-x ielm is the builtin Inferior Emacs Lisp Mode. It's relatively featureless, but can definitely come in handy. (Esp. for learning Elisp)
SLIME, the Superior Lisp Interaction Mode for Emacs, is mostly a joke on the whole "inferior" process name. SLIME is used primarily for Common Lisp (although it can be used with other lisps to varying degrees via extensions). It boasts a large variety of "superior" functions, including debugging, interactive REPLs, and various IDE like functions.
CIDER, the Clojure Interactive Development Environment that Rocks for Emacs, is something like SLIME but for Clojure. (Clojure itself being a rather curious lisp that needs some extra work to interface with)