For future reference, here's a script that one can use to check (unfortunately, only with one's own eyes) if an implementation behaves as expected.

SBCL e.g. does (with the change for consistency in place). Here's the output of the script:

====
UIOP/RUN-PROGRAM:RUN-PROGRAM ("./stdout.sh") :OUTPUT :INTERACTIVE
stdout
UIOP/RUN-PROGRAM:RUN-PROGRAM ("./stdout.sh") :OUTPUT :INTERACTIVE :FORCE-SHELL T
stdout
UIOP/RUN-PROGRAM:LAUNCH-PROGRAM ("./stdout.sh") :OUTPUT :INTERACTIVE
stdout
UIOP/RUN-PROGRAM:RUN-PROGRAM "./stdout.sh" :OUTPUT :INTERACTIVE
stdout
UIOP/RUN-PROGRAM:RUN-PROGRAM "./stdout.sh" :OUTPUT :INTERACTIVE :FORCE-SHELL T
stdout
UIOP/RUN-PROGRAM:LAUNCH-PROGRAM "./stdout.sh" :OUTPUT :INTERACTIVE
stdout

UIOP/RUN-PROGRAM:RUN-PROGRAM ("./stdout.sh") :OUTPUT NIL
UIOP/RUN-PROGRAM:RUN-PROGRAM ("./stdout.sh") :OUTPUT NIL :FORCE-SHELL T
UIOP/RUN-PROGRAM:LAUNCH-PROGRAM ("./stdout.sh") :OUTPUT NIL
UIOP/RUN-PROGRAM:RUN-PROGRAM "./stdout.sh" :OUTPUT NIL
UIOP/RUN-PROGRAM:RUN-PROGRAM "./stdout.sh" :OUTPUT NIL :FORCE-SHELL T
UIOP/RUN-PROGRAM:LAUNCH-PROGRAM "./stdout.sh" :OUTPUT NIL

UIOP/RUN-PROGRAM:RUN-PROGRAM ("./stdout.sh") :ERROR-OUTPUT :INTERACTIVE
UIOP/RUN-PROGRAM:RUN-PROGRAM ("./stdout.sh") :ERROR-OUTPUT :INTERACTIVE :FORCE-SHELL T
UIOP/RUN-PROGRAM:LAUNCH-PROGRAM ("./stdout.sh") :ERROR-OUTPUT :INTERACTIVE
UIOP/RUN-PROGRAM:RUN-PROGRAM "./stdout.sh" :ERROR-OUTPUT :INTERACTIVE
UIOP/RUN-PROGRAM:RUN-PROGRAM "./stdout.sh" :ERROR-OUTPUT :INTERACTIVE :FORCE-SHELL T
UIOP/RUN-PROGRAM:LAUNCH-PROGRAM "./stdout.sh" :ERROR-OUTPUT :INTERACTIVE

UIOP/RUN-PROGRAM:RUN-PROGRAM ("./stdout.sh") :ERROR-OUTPUT NIL
UIOP/RUN-PROGRAM:RUN-PROGRAM ("./stdout.sh") :ERROR-OUTPUT NIL :FORCE-SHELL T
UIOP/RUN-PROGRAM:LAUNCH-PROGRAM ("./stdout.sh") :ERROR-OUTPUT NIL
UIOP/RUN-PROGRAM:RUN-PROGRAM "./stdout.sh" :ERROR-OUTPUT NIL
UIOP/RUN-PROGRAM:RUN-PROGRAM "./stdout.sh" :ERROR-OUTPUT NIL :FORCE-SHELL T
UIOP/RUN-PROGRAM:LAUNCH-PROGRAM "./stdout.sh" :ERROR-OUTPUT NIL

UIOP/RUN-PROGRAM:RUN-PROGRAM ("./stderr.sh") :OUTPUT :INTERACTIVE
stderr
UIOP/RUN-PROGRAM:RUN-PROGRAM ("./stderr.sh") :OUTPUT :INTERACTIVE :FORCE-SHELL T
stderr
UIOP/RUN-PROGRAM:LAUNCH-PROGRAM ("./stderr.sh") :OUTPUT :INTERACTIVE
UIOP/RUN-PROGRAM:RUN-PROGRAM "./stderr.sh" :OUTPUT :INTERACTIVE
stderr
UIOP/RUN-PROGRAM:RUN-PROGRAM "./stderr.sh" :OUTPUT :INTERACTIVE :FORCE-SHELL T
stderr
UIOP/RUN-PROGRAM:LAUNCH-PROGRAM "./stderr.sh" :OUTPUT :INTERACTIVE

UIOP/RUN-PROGRAM:RUN-PROGRAM ("./stderr.sh") :OUTPUT NIL
UIOP/RUN-PROGRAM:RUN-PROGRAM ("./stderr.sh") :OUTPUT NIL :FORCE-SHELL T
UIOP/RUN-PROGRAM:LAUNCH-PROGRAM ("./stderr.sh") :OUTPUT NIL
UIOP/RUN-PROGRAM:RUN-PROGRAM "./stderr.sh" :OUTPUT NIL
UIOP/RUN-PROGRAM:RUN-PROGRAM "./stderr.sh" :OUTPUT NIL :FORCE-SHELL T
UIOP/RUN-PROGRAM:LAUNCH-PROGRAM "./stderr.sh" :OUTPUT NIL

UIOP/RUN-PROGRAM:RUN-PROGRAM ("./stderr.sh") :ERROR-OUTPUT :INTERACTIVE
UIOP/RUN-PROGRAM:RUN-PROGRAM ("./stderr.sh") :ERROR-OUTPUT :INTERACTIVE :FORCE-SHELL T
UIOP/RUN-PROGRAM:LAUNCH-PROGRAM ("./stderr.sh") :ERROR-OUTPUT :INTERACTIVE
UIOP/RUN-PROGRAM:RUN-PROGRAM "./stderr.sh" :ERROR-OUTPUT :INTERACTIVE
UIOP/RUN-PROGRAM:RUN-PROGRAM "./stderr.sh" :ERROR-OUTPUT :INTERACTIVE :FORCE-SHELL T
UIOP/RUN-PROGRAM:LAUNCH-PROGRAM "./stderr.sh" :ERROR-OUTPUT :INTERACTIVE

UIOP/RUN-PROGRAM:RUN-PROGRAM ("./stderr.sh") :ERROR-OUTPUT NIL
UIOP/RUN-PROGRAM:RUN-PROGRAM ("./stderr.sh") :ERROR-OUTPUT NIL :FORCE-SHELL T
UIOP/RUN-PROGRAM:LAUNCH-PROGRAM ("./stderr.sh") :ERROR-OUTPUT NIL
UIOP/RUN-PROGRAM:RUN-PROGRAM "./stderr.sh" :ERROR-OUTPUT NIL
UIOP/RUN-PROGRAM:RUN-PROGRAM "./stderr.sh" :ERROR-OUTPUT NIL :FORCE-SHELL T
UIOP/RUN-PROGRAM:LAUNCH-PROGRAM "./stderr.sh" :ERROR-OUTPUT NIL
====

And this is the script:

====
(load "common-lisp/asdf/build/asdf.lisp")

(defmacro verbose-do ((f &rest args))
  `(progn
     (format t "~s ~{~s~^ ~}~%" ',f (list ,@args))
     (,f ,@args)))

(loop
   :for script :in ‘(“./stdout.sh" “./stderr.sh")
   :do
   (loop
      :for (specifier . mode)
      :in '((:output . :interactive) (:output . nil)
            (:error-output . :interactive) (:error-output . nil))
      :do (progn
            (verbose-do (uiop:run-program (list script) specifier mode))
            (verbose-do (uiop:run-program (list script) specifier mode :force-shell t))
            #-clisp (uiop:wait-process
                     (verbose-do
                      (uiop:launch-program
                       (list script) specifier mode)))

            (verbose-do (uiop:run-program script specifier mode))
            (verbose-do (uiop:run-program script specifier mode :force-shell t))
            #-clisp (uiop:wait-process
                     (verbose-do
                      (uiop:launch-program
                       script specifier mode)))
            (terpri))))

(uiop:quit 0)
====

With these two helpers:

- stdout.sh: 

====
#!/bin/sh

echo stdout
====

- stderr.sh:

====
#!/bin/sh

echo stderr 1>&2
====