My computer update

To be clear, software update is to install software to revises the macOS currently running on the Mac; update Catalina 10.15.1 to Catalina 10.15.7, for example.

To update your current macOS, click the Apple  icon > About This Mac and then click Software Updates.... If there are any updates available for your Mac, they will be listed and you can apply them when you like.  Software updates may be set to occur automatically.  If no updates are presented, then it may be assumed that none are available for your current OS.

A software upgrade replaces the currently installed macOS with a newer, differently named version; upgrade from 10.13 High Sierra to 10.14 Mojave, for example, or from 10.15 Catalina to macOS 11 Big Sur. Upgrades do not happen automatically. An upgrade must be initiated by a user with admin privileges.

Use Software Update to update or upgrade macOS, including built-in apps like Safari. 

Please see >: Update macOS on Mac - Apple Support

Yes, it will first list any updates that are available for your current version of the OS. Once those updates are installed, run the process again to check for any additional updates that are available. Do this until the updater finds no more updates.

The final version of High Sierra will be 10.13.6.

Beyond that, you'll have to upgrade the OS.

The macOS version you can upgrade to depends on the year your Mac was released.

Click the  (Apple) menu at the top of your screen and choose About This Mac.

Check the Compatibility of your Mac with newer versions of macOS:

➡️ macOS 10.14 Mojave is compatible with the Macs listed here

➡️ macOS 10.15 Catalina is compatible with the Macs listed here

➡️ macOS 11 Big Sur is compatible with the Macs listed here 

➡️ macOS 12 Monterey is compatible with the Macs listed here

➡️ macOS 13 Ventura is compatible with the Macs listed here

Click the  (Apple) menu at the top of your screen and choose About This Mac.