Update for osmac 10.13.6

Good work, latest 10.13 is 10.13.6 (17G14042) (November 12, 2020).

So maybe you're looking for Upgrades instead of Updates...

Next 2 would be ...

macOS Mojave 10.14.6 - Technical Specifications

General Requirements

OS X 10.8 or later

2GB of memory

12.5GB of available storage (OS X El Capitan 10.11.5 or later)*

Some features require an Apple ID; terms apply.

Some features require a compatible Internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Mojave:

MacBook (Early 2015 or newer)

MacBook Air (Mid 2012 or newer)

MacBook Pro (Mid 2012 or newer)

Mac mini (Late 2012 or newer)

iMac (Late 2012 or newer)

iMac Pro (2017)

Mac Pro (Late 2013; Mid 2010 and Mid 2012 models with recommended Metal-capable graphics cards)

https://itunes.apple.com/us/app/macos-mojave/id1398502828?mt=12

Thanks to MartinR Terminal command…

softwareupdate --fetch-full-installer --full-installer-version 10.14.6

It will place a copy of the installer in your Applications folder and you can use that to create a bootable installer.

MacOS Catalina 10.15.7 - Technical Specifications

General Requirements

OS X 10.9 or later

4GB of memory

12.5GB of available storage (OS X El Capitan 10.11.5 or later)*

Some features require an Apple ID; terms apply.

Some features require a compatible internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Catalina:

MacBook (Early 2015 or newer)

MacBook Air (Mid 2012 or newer)

MacBook Pro (Mid 2012 or newer)

Mac mini (Late 2012 or newer)

iMac (Late 2012 or newer)

iMac Pro (2017)

Mac Pro (Late 2013 or newer)

How to download macOS - Apple Support

https://apps.apple.com/gb/app/macos-catalina/id1466841314?ls=1&mt=12

macappstores://apps.apple.com/app/macos-catalina/id1466841314?ls=1&mt=12

How to upgrade to macOS Catalina – Apple Support

And caution on 10.15 or higher, to see which Apps will no longer work in 10.15 get Go64...

https://www.stclairsoft.com/Go64/

If you get a corrupted message...

Naw, it's not damaged, it's just that you have an old copy already in Applications, there are 2 cures...

If you’re short of bandwidth or data… Disconnect from the Internet & set the Date back to 2014, then you can run the Install MacsOS Mohave App in Applications, so expired Certificates are not expired.

Or... trash the Install MacsOS Mojave.app in Applications then a new copy can be downloaded.

There haven't been any for years, but under the Apple logo at top left>App Store>Updates do any show there?

What build# shows when you click on Version?

Did you clock on the 10.13.6 text to expose the Build# ?

Perhaps they were speaking of Upgrades instead of Updates?

Which exact Mac do you have? It's right below the Version?

Great news & good luck my friend! :)