How to download OS catalina or Mojave installer file without opening in Settings - Software update window?

I have currently OS Catalina on this laptop

I dont want to update, I simply want to download the OS (Mojave would be better) and create bootable drive for my friend.

From your Catalina machine you can use the Terminal.app to download the full installer, copy and paste::

softwareupdate --fetch-full-installer --full-installer-version 10.15.1

for the Mojave, copy and paste:

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

When successfully download it will be sitting in your applications folder as expected

"Install macOS Mojave.app"

carry on with your createinstallmedia command

How to create a bootable installer for macOS - Apple Support

On a Mac that has not been upgraded to Catalina, and in my case, still running Mojave, the System Preferences : Software Update panel will show a Upgrade Now button for Catalina. Instinct suggests that this would be a runaway train and just perform the upgrade — but that is not the case. The end result is that a familiar operating system install panel automatically appears, as though one had direct downloaded the installer from the Mac App Store. Once cancelled, you have a full Catalina installer in /Applications.

This is not theory. I actually did the first paragraph and created a bootable USB stick from the full installer.

One does not do this for incremental updates for the same operating system as that is a runaway train that does not stop until done.

Have you tried this way of getting Mojave installer -- https://support.apple.com/macos/mojave ???

Good luck...