When making a bootable drive for Big Sur . . .

DanPeters wrote:

Do I download Big Sur to my Laptop to make the bootable installer or to the Thumb drive.

Yes.

App Store:

https://apps.apple.com/us/app/macos-big-sur/id1526878132?ls=1&mt=12

If it automatically launches you quit it like any other app.

How to create a bootable installer for macOS - Apple Support

If you name the incoming thumb drive exactly MyVolume, you do not need to modify the scripts at all.

Also, you can copy the entire command-line from the article (be sure you get it all) and paste directly into the Terminal window.

You have to place the downloaded Installer image on your hard drive, because step 1 of creating the Bootable Thumb drive is to ERASE the thumb drive.