diff --git a/Doc/c-api/veryhigh.rst b/Doc/c-api/veryhigh.rst
--- a/Doc/c-api/veryhigh.rst
+++ b/Doc/c-api/veryhigh.rst
@@ -32,13 +32,14 @@
    prepared exactly as those which are passed to a C program's :cfunc:`main`
    function.  It is important to note that the argument list may be modified (but
    the contents of the strings pointed to by the argument list are not). The return
-   value will be the integer passed to the :func:`sys.exit` function, ``1`` if the
-   interpreter exits due to an exception, or ``2`` if the parameter list does not
-   represent a valid Python command line.
+   value will be ```0``` if the interpreter exits normally (ie, without an 
+   exception), ``1`` if the interpreter exits due to an exception, or ``2`` 
+   if the parameter list does not represent a valid Python command line.
 
-   Note that if an otherwise unhandled :exc:`SystemError` is raised, this
+   Note that if an otherwise unhandled :exc:`SystemExit` is raised, this
    function will not return ``1``, but exit the process, as long as
-   ``Py_InspectFlag`` is not set.
+   ``Py_InspectFlag`` is not set.  Further, be aware that the builtin function
+   ``exit()`` is implemented by raising a :exc:`SystemExit` exception.
 
 
 .. cfunction:: int PyRun_AnyFile(FILE *fp, const char *filename)
@@ -82,7 +83,7 @@
    there was an error, there is no way to get the exception information. For the
    meaning of *flags*, see below.
 
-   Note that if an otherwise unhandled :exc:`SystemError` is raised, this
+   Note that if an otherwise unhandled :exc:`SystemExit` is raised, this
    function will not return ``-1``, but exit the process, as long as
    ``Py_InspectFlag`` is not set.
 
diff --git a/Python/pythonrun.c b/Python/pythonrun.c
--- a/Python/pythonrun.c
+++ b/Python/pythonrun.c
@@ -76,7 +76,7 @@
 int Py_DebugFlag; /* Needed by parser.c */
 int Py_VerboseFlag; /* Needed by import.c */
 int Py_InteractiveFlag; /* Needed by Py_FdIsInteractive() below */
-int Py_InspectFlag; /* Needed to determine whether to exit at SystemError */
+int Py_InspectFlag; /* Needed to determine whether to exit at SystemExit */
 int Py_NoSiteFlag; /* Suppress 'import site' */
 int Py_BytesWarningFlag; /* Warn on str(bytes) and str(buffer) */
 int Py_DontWriteBytecodeFlag; /* Suppress writing bytecode files (*.py[co]) */