Symptoms

On your ISO external keyboard (European, with the big Enter key), the characters on the left of 1 is inverted with the one on the right of the left Shift.

This usually means that macOS has not identified your keyboard type correctly. You can check this with the Keyboard Viewer:

Mac keyboard viewer with a wrong ISO layout

When pressing a key on your external keyboard, it will update to what macOS thinks your keyboard looks like. Here the keyboard had been identified as a Macintosh one instead of a standard one.

Fix

It looks like the selected input source can interfere with the automated keyboard identification. Identify the keyboard manually if that’s the case.

Start the Keyboard Setup Assistant

Change keyboard layout button

Only if you cannot see this option, you may need to remove the keyboard type preference file and reboot the Mac. For example, in a terminal:

sudo rm /Library/Preferences/com.apple.keyboardtype.plist

Double-check the keyboard type

Follow the Keyboard Setup Assistant instructions, but double-check that the keyboard is identified correctly.

Mac Keyboard Assistant wrong layout identified

If you are using a standard European PC keyboard, it should be identified as ISO/IEC 9995.

If you are using a European Macintosh keyboard, it should be identified as ISO/Macintosh.

Skip the automated detection if it is not working

If the keyboard is not identified correctly, go back and press random keys until you can skip the automated detection.

Skip automated identification

Now you can choose the correct layout, here a standard European PC keyboard (ISO/IEC 9995).

mac-keyboard-viewer-wrong-layout

Hopefully, the keys are now behaving like expected, both on your external keyboard and your MacBook one. The Keyboard Viewer layout should match the one of your physical keyboard.

Mac keyboard viewer with a ISO/IEC 9995 layout