FUNCALL is useful when the programmer knows the length of the argument
list, but the function to call is either computed or provided as a
parameter.  For instance, a simple implementation of MEMBER-IF (with
none of the fancy options) could be written as:

(defun member-if (predicate list)
  (do ((tail list (cdr tail)))
      ((null tail))
   (when (funcall predicate (car tail))
     (return-from member-if tail))))

The programmer is invoking a caller-supplied function with a known
argument list.

APPLY is needed when the argument list itself is supplied or computed.
Its last argument must be a list, and the elements of this list become
individual arguments to the function.  This frequently occurs when a
function takes keyword options that will be passed on to some other
function, perhaps with application-specific defaults inserted.  For
instance:

(defun open-for-output (pathname &rest open-options)
  (apply #'open pathname :direction :output open-options))

FUNCALL could actually have been defined using APPLY:

(defun funcall (function &rest arguments)
  (apply function arguments))