heavens, if cf 5 III could rightly be titled, "Automatic External Manual Flash", what could they call cf5 II? Automatic External Manual Auto Flash mode

The 580EXII owner's manual does a fine job of labelling the functions controlled by CFn-5
ETTL
TTL
External metering: Auto
External metering: manual
and also explicitly referring owners to the page which further explains what that selection does.
External metering: Auto is explained on p.30, depicted here
Nothing to fault with their documentation per se.
Canon is rather unique in referring to flash photosensor mode as 'External' (from the camera metering) rather than simply referring it to 'Auto' mode which has been a term used by flash manufacturers for decades! When Olympus first launched TTL flash two decades ago, it termed that mode 'TTL Automatic' for the camera TTL flash metering vs. the 'Normal Automatic' of the photosensor in the flash.


