This information is also available on Google's support page.
Your question focuses on the definitions of two things:
Android Version Updates : these are the updates to new numbered versions of Android, such as Android 13 you described, that usually include things like new features and design changes.
Security Updates : these updates are distributed on a monthly basis and are meant to provide critical improvements needed to keep the operating system secure.
You can continue to use your phone without either of these updates, but as you specified, your phone may be considered "less secure" than others with more recent updates. In practice, however, many people use devices for long periods of time after they're out of security update support life. In this case, the responsibility for security is yours, rather than Google's.