Earth ground is simply the earth with any kind of conductive metal pounded deeply enough into it (usually at least 6' in moist earth). AC ground becomes referenced to Earth ground at the point which the ground bus from the distributed AC system (local or portable) gets connected to the local earth ground. So for all intents and purposes in this discussion they will be functionally equivalent in a properly wired sound system, assuming that the bond between the two is secure.
Earth ground is our local voltage reference. The earth is the biggest chunk of anything we have around to stick a metal stake into and call the place of lowest voltage potential so that we can whip out our Flukes and have a place to put the black test lead. Our first clue was that the ground is the place lightning always seemed to lust after. If we could somehow stretch a voltmeter between the moon and the earth we would probably see a significant difference in voltage or "potential". "Ground", in an AC system on the moon, would still be referenced to the moon's soil even if there was a huge voltage potential between the moon and earth. 100 volts to ground on the moon would still be "100 volts to ground" even if there were a million volts of potential between the earth and the moon. On the moon, the moon's ground would be the local reference.
Getting electrocuted from an appliance was a lot easier before a local ground wire was added to our AC systems. This ground wire is distributed in the AC service and is internally attached to the chassis of appliances so that if the appliance suffers a short from the internal circuitry to the grounded chassis of the appliance, the short would blow a fuse or trip a breaker disabling the AC power. This, as opposed to the electrically hot chassis becoming an electrocution waiting to happen as soon as someone touches anything grounded while in contact with the electrically hot chassis. "AC Ground" as it appears in our electrical systems is a safety connection and is NOT intended to carry current. AC Ground, because it is not intended to carry current, also happens to serve as a conveniently distributed reference we can use for our audio systems.
Generally the first thing we do as audio people when setting up our portable AC power distribution systems ("PD" or "distro" in touring lingo) in a venue is to have the house electrician connect it into the nearest available AC service panel which hopefully has a good ground connection. One should always inspect what is being called the "ground" for your portable AC distribution system although you are more likely to get a good ground in venues of more recent vintage built to more rigorous electrical standards. If the ground connection or its source looks dubious, an alternative should be found. Conventional wisdom has dictated that a water pipe or standpipe is a good source of ground based on the logic that eventually the metal pipe will enter the earth on its way to or from the building via the water supply or sewage systems. A "water pipe ground" isn't always reliable in some newer buildings because these pipes are often connected to PVC plastic pipe at some point (breaking continuity) before it actually enters "earth". Plastic is not a very good conductor of electricity. If you feel you have to connect to water pipe ground, inspect the actual path to earth.
In some older smaller buildings the source of the local distributed ground system is simply a metal stake driven into the ground outside the building with a cable running inside to the main service box. If the stake is too short (less than 3'), or the stake area is dry, the AC ground will be less effective. Sometimes a metal rod is driven into the earth prior to the poured concrete basement floor. It just appears as a metal rod poking up from the cement floor with a cable clamped to it running from there into the main service box - the box chassis itself sometimes serving as the bond between neutral and ground which should also be inspected. Sometimes this box chassis work is poorly executed and you should inspect it, especially if you are having hum problems (check to see if they bothered to scrape the paint off the box chassis where contacts are made). It is essential to personally inspect what is being called your source of local earth ground and its entire path to your AC distribution system. If someone were to get electrocuted, you could be held liable if your system is not properly grounded. It also helps alleviate that nagging feeling in the back of your mind that there's maybe something you've overlooked. Newer buildings often have a large metal grid laid into the earth nearby as a "ground" source. A cable is then bonded to the grid and run to the power transformer in or very near the building.
The neutral produced by the secondary winding of the local AC power transformer is electrically bonded to the building's "earth ground", usually at the transformer. Now the building's AC service is said to be ground referenced. The hot to neutral voltage will read the same as hot to ground voltage at this main distribution point because neutral and ground are bonded or shorted together there. Very often this neutral-ground bond takes place outside the building at the transformer and the main neutral and ground service cables enter the building separately.
The simplicity of a good earth ground was clearly illuminated for me many years ago by an electrician known as "Animal". We were on a sandy site near the edge of a tidal bay on a full blown live outdoor HBO production, all powered off of several generators. The production had been having problems getting a good ground from the sandy soil even before I arrived with the PA system. Unfortunately, some poor stagehand had driven a forklift into the bay off of a narrow service road into about 4' of water. Animal, seizing an opportunity, waded out to the forklift with a green Camlock "tail" and clamped it to the metal forklift, hauled a chunk of 2/0 feeder cable out into the water from the central ground point of the show's main AC power distro and attached it to the tail. "Now we've got an excellent ground! It doesn't get any better than that!", he proudly announced. In his honor, I recreated this feat not with a forklift but with a large section of metal scaffolding frame in Manila, Philippines where they now recreate it in my honor every time they use a particular venue by the ocean with generators.
When is AC Ground not Earth Ground? A sound system can have the main earth ground service connection lifted and not buzz because down stream of that connection, the AC ground is still universally distributed and connected to all of the gear as the common shared reference even though the entire system is essentially floating from earth ground. This is a highly dangerous and illegal practice and absolutely not recommended but it I have seen it a few times out there. Although in the US, Europe and many areas of the world, audio equipment must be earth grounded for safety reasons, an audio system does not need an earth ground in order to work properly. Most consumer stereo systems do not even have earth ground connections. In Japan, most standard AC wall sockets do not have a ground connection.