This is correct. msdos.sys was a text file with configuration values, which could be set to either auto-start Windows after running autoexec.bat, or not. In the former case, exiting Windows would stop at the "now safe to turn off your computer" screen. In the latter case, startup would go to a DOS command prompt, and Windows could be started from there, and exiting it would go back to DOS.
Those two cases got conflated by the ability to start Windows from within autoexec.bat, which wasn't the Microsoft default but was a fairly common setup from some OEMs. To the OS, that's the case of starting Windows separately, but to the user, it looks like the auto-starting case.
You could also make it "boot into DOS" by adding command.com as the last thing autoexec.bat would invoke. That way you end up in the shell, and exiting it would boot Windows.
Those two cases got conflated by the ability to start Windows from within autoexec.bat, which wasn't the Microsoft default but was a fairly common setup from some OEMs. To the OS, that's the case of starting Windows separately, but to the user, it looks like the auto-starting case.