Is it possible to screen capture a specific window (also possibly of another process)?
Currently I am capturing the entire desktop of a specific monitor, however what I truly want is to capture the content of a specific window (regardless of its position).
Yes it is. All what you need is get handle to window which you want to capture and use WinAPI function PrintWindow for example:
// Get the window handle of calculator application.
HWND hWnd = ::FindWindow( 0, _T( "Calculator" ));
// Take screenshot.
PrintWindow( hWnd, getDC(hWnd), 0 );
Here you have PrintWindow documentation.