Choose display when doing a screen capture with external display
You might use ⇧⌘4 (Save picture of selected area as a file) and just drag the selection around one display.

screencapture -m only captures the main display:

-m      Only capture the main monitor, undefined if -i is set.


I don't know if -S supposed to capture the display of the selected window, but options like -Sw or -SW only seemed to capture the selected window.

-S      In window capture mode, capture the screen instead of the window.
-w      Only allow window selection mode.
-W      Start interaction in window selection mode.


-R (rect) captures a specified area:

screencapture -R0,0,1920,1080 /tmp/screencapture.png