I think Rainer's answer gets this right, but since the question appeared in a comment on my answer to another question, I'll include (an update to) my response from that comment.
A symbol is an actual object. You can inspect it, you can create them with make-symbol, etc. Importantly, symbols are one of the primary components of source code in Common Lisp. Function names, especially in the context that this question arose in (arguments to the function special operator) are either symbols or lists of the form (setf symbol) according to the glossary entry:
function name n. 1. (in an environment) A symbol or a list (setf symbol) that is the name of a function in that environment. 2. A
symbol or a list (setf symbol).
Function is a special operator that doesn't evaluate its arguments, so passing a symbol or setf list means something like:
(function car)
(function (setf car))
and not:
(function 'car)
(function '(setf car))
Now, lexical variables, e.g., x in (let ((x 42)) x), while represented by symbols in the source code, don't actually have any connection with the symbol at runtime. The compiled version of (let ((x 42)) x) doesn't need to know anything about the symbol x. Intuitively, this makes sense, because we'd expect the code (let ((y 42)) y) to compile to the same thing. However, when a variable is special, there is a connection with the symbol. The difference is clearest with:
(let ((x 42))
(symbol-value x))
;=> NIL
(let ((x 42))
(declare (special x)) ; or (defparameter x ...) or (defvar x ...) earlier
(symbol-value x))
;=> 42
We'd expect the same thing to be true of lexically scoped functions, e.g., the following code causes an error because there's no connection between the symbol x at runtime and the local function:
(flet ((x () 42))
(symbol-function 'x)) ; ERROR, no function value for symbol x
But even so, we can still do:
(flet ((x () 42))
(function x))
This is because function is special operator and can access the environment where is occurs. That means that (because it's special, and the implementation makes it work) it can know that x is defined as function here. It may be interesting to note, now, that since flet and labels are defined to take a function name, you can do:
(flet (((setf kar) (value kons)
...))
...)