plugin development - What is a settings group actually for? in WordPress

Sanitization is secondary function. Main is:

The register_setting and unregister_setting functions add and remove options from a whitelist of allowed options that the form is able to save. They can also name a sanitize callback function as a security measure to check each option's value. ( Register settings )

Technically $option_group argument is used for:

• array key in global array of whitelisted options
• part of filter name to run sanitization callback