When notifications show that there are updates available for the computer, macOS will display any major OS upgrades at the top while putting the minor version updates at the bottom of the window. This can be difficult to notice.
To run the macOS updates for the current OS without upgrading the OS, follow these steps:
For macOS 13 (Ventura)
1. Open System Settings and click on General → Software Update.
2. Under the macOS upgrade option, scroll all the way to the bottom, there should e a statement about additional updates underneath.
3. Click on "More Info..." under the other updates and the available updates should be presented.
4. Click Install Now to begin the installation process through to completion.
If you are asked for a password...
NOTE: On some computers, it may prompt for a password. If this occurs, it will be your regular login password for the computer (not an administrator password). If your regular password is rejected and you are sure you typed your password correctly, then you may have changed your MyID password since you first logged into the computer and the new password is out of sync. Try the original password if you can remember it, or contact helpdesk@franklin.uga.edu and we can assist in syncing the passwords. 
For macOS 12 (Monterey) and below
1. Open System Preferences and click on Software Update
2. Under the macOS upgrade option, there should be a statement about additional updates underneath.
3. Click on "More Info..." under the other updates and the available updates should be presented.
4. Click Install Now to begin the installation process through to completion.
If you are asked for a password...
NOTE: On some computers, it may prompt for a password. If this occurs, it will be your regular login password for the computer (not an administrator password). If your regular password is rejected and you are sure you typed your password correctly, then you may have changed your MyID password since you first logged into the computer and the new password is out of sync. Try the original password if you can remember it, or contact helpdesk@franklin.uga.edu and we can assist in syncing the passwords.