Keyboard shortcuts for switching desktops between multiple displays not working
'Displays have separate Spaces' would appear to be the method you do require, but in order for it to work, you must have more Spaces than screens.

Then your key commands will switch the screen the cursor is currently in to your requested Space.

Don't rely on the numbers being accurate until you have set up your full set of Spaces &amp; then, in order to then keep the numbering as you intended, make sure 'Automatically rearrange Spaces based on most recent use' is off.

You can drag Spaces into the desired order by invoking Mission Control; take the cursor to the top of a screen &amp; the desktop numbers will expand to show a thumbnail of contents. You can then drag them to your required order &amp; they will re-number automatically.

One more thing, which often catches people out - Spaces only work as intended if any given app only occupies any one Space. If you try to spread an app to 2 or more Spaces simultaneously, it breaks behaviour.

The alternative working method [the one I actually prefer] is to disable 'Displays have separate Spaces', then each 'desktop' becomes a pair of screens, which move together. So you have 2 screens simultaneously showing Desktop 1, then both switch to Desktop 2, etc in tandem - in effect making each Space double-sized. Apps then stay on the screen &amp; the Space they are assigned, so long as you don't disconnect one screen.