I knew you would get good information from neilpzz, so this is only a supplement:
Safe Mode is a stripped down version of Windows. Only the essential guts of Windows is running. There is no third party software. Safe Mode is used to determine whether third party software is causing a problem, and gives you the opportunity to identify the problem-causing software. You don't want to run your computer in Safe Mode.
S Mode is a version of Windows with limitations: You can only install software that comes from Microsoft Store and you can only use Microsoft Edge as your browser. In all other respects, it's regular Windows. It's for people who need that extra security.