In short, the offline installer link at https://www.opera.com/download gives me the 32-bit offline installer instead of the 64-bit (when visiting the page with Chrome Stable 64-bit on Windows 10 64-bit).

Thanks @burnout426,

And via https://www.opera.com/download, "Download the offline package", I auto-get "Opera_68.0.3618.125_Setup.exe" (32-bit) although my user agent is

from current Opera:

Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/81.0.4044.138 Safari/537.36 OPR/68.0.3618.125

from current installed MS Edge:

Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/70.0.3538.102 Safari/537.36 Edge/18.18363

and the OS Win64 or x64 version should be detected - and the 64-bit installer "Opera_68.0.3618.125_Setup_x64.exe" should be auto-detected and downloaded.

Someone should change this on Opera website, or isn't it?

The 32-bit installer will detect your system configuration and install the appropriate Opera package

For the web installer. But, I can't confirm this for the offline installer at https://www.opera.com/download. It's giving me the same file as Opera_68.0.3618.125_Setup.exe in http://get.opera.com/ftp/pub/opera/desktop/68.0.3618.125/win/, which only contains the 32-bit binaries and only installs them (confirmed via task manager that it's 32-bit Opera). In short, the offline installer link at https://www.opera.com/download gives me the 32-bit offline installer instead of the 64-bit (when visiting the page with Chrome Stable 64-bit on Windows 10 64-bit).

In my case at least, I'd definitely want to get the 64-bit offline installer instead.

Can you confirm?

They're for 64-bit versions of Win7 and newer. It's what you should use by default if you're going to use the offline installer and have 64-bit Windows.

But the normal download page https://www.opera.com/download - choose "Download the offline package" - auto-selects and downloads "Opera_68.0.3618.125_Setup.exe" and installs into the 64-bit directory "C:\Program Files" and not into the 32-bit directory "C:\Program Files (x86)"

So finally both are 64-bit versions or isn't?

If not and I should choose _x64.exe - why does the download page not auto-select this version (should be able to because of JavaScript info)?

Are the _x64 bit versions for older 64-bit OS like Windows 7 or 8?

They're for 64-bit versions of Win7 and newer. It's what you should use by default if you're going to use the offline installer and have 64-bit Windows.

When I want to disable the auto-update I have to start Opera with

To disable the updater, rename opera_autoupdate.exe in the latest version folder in Opera's install directory. This will break checking for updates on the opera://about and opera://update pages. But, you can monitor https://blogs.opera.com/desktop/ and even subscribe to its RSS feed.

You will need to rename the updater after each time you update Opera.

http://get.opera.com/ftp/pub/opera/desktop/68.0.3618.125/win/

Make sure to use the https version instead so that it's secure.

What is the difference between the Setup and Autoupdate?

No need to use the autoupdate files. I've never used them. I assume it's the installer with just the necessary patches for updating from the previous version (or previous few versions) so that the download is a little smaller. Not sure if Opera's autoupdater fetches those or just the patches etc. But, again, no need to use them yourself.