Traditionally, "auto" flash utilizes a light sensor built into the flash unit. The flash unit measures its own light reflecting off the subject, in real time, and turns off the bulb when sufficient light has been produced. Old-fashioned flash units work this way and usually work very well. The camera's aperture and ISO need to be set to match the settings on the flash unit.
The original 580EX does not have the built-in light sensor or circuitry to operate this way. It's a dedicated flash that requires the camera's TTL (film) or E-TTL (digital) system to tell it how much light to produce. The recently released 580EX II is the first Canon Speedlite with the option to use either TTL, E-TTL or traditional auto modes, and has the sensor and circuitry to enable this.
TTL and E-TTL systems can be described as forms of "automatic flash metering", but they are different from "auto" flash in the traditional sense.
If you are using E-TTL with +/- FEC, it's still E-TTL. FEC simply adjusts the output up or down from what it considers "normal".
Manual flash is entirely different. In manual mode, you tell the flash how much light to produce. Period. Full power, half power... all the way down to 1/128 power. There is no metering of any kind involved.
High speed sync is a different functionality. HSS can be used in E-TTL or manual mode.
Much more information on all of this in The EOS Flash Bible (link in my signature).