OS X: Can the App Switcher be modified to be more intuitive?
Context

OS X has two modes, depending on whether you adjusted the 'Displays have separate Spaces' in System Preferences > Mission Control.

In the default (enabled) mode you'll find that which ever screen has focus (i.e the front window is on that screen and you can type into it) will have the app switcher. This is indicated by the fact the Menu Bar at the top is sold rather than translucent.

In the disabled mode you'll find which ever screen is allocated as the primary display in System Preferences > Displays > Arrangement will have all of the OS related GUI on it, i.e. the Menu Bar, Dock, and other system level interactions will only show on that screen.



Answer

You can change your application switcher with Witch to allow more Windows like window switching rather than application switching. Maybe this would be more intuitive to  you, alternatively try using mission control F3 which shows you all the applications on each screen on the screen they are on.