Here's the functional difference. In a proper 3-prong grounded outlet, the Ground line is connected by a bare copper wire in the cable to a Ground point in the Breaker Panel. This line has NO other purpose and should NEVER have any current running through it except in abnormal emergency conditions. The Breaker Panel Ground is connected by heavy cable to a true Earth Ground in the form of an existing buried water pipe in the ground or, preferably (required in some areas) a dedicated Ground rod buried in the ground. It is truly at zero volts potential compared to the earth at all times.
In a device plugged into a Grounded outlet with proper wiring, the Ground lead in the device's cord is connected to the exterior chassis of the device, and likely also to some portion of the internal chassis. The effect is that any conductive portion of the device that is normally accessible is always Grounded. The Hot and Neutral lines of the power supply are connected only to active circuit elements in the device. In the event of a malfunction that allows a supply voltage to contact the exposed surface, two things happen simultaneously. One is that the connection provides a VERY low-resistance current path from the Hot lead to Ground, allowing a very heavy current to flow through that circuit. The current normally is so large that the breaker supplying the Hot lead is overloaded and trips, stopping all current flow and removing the voltage. The second effect is that, because the Ground lead has such low resistance, the voltage present on the device's exterior surface that you might be touching, compared to true Ground, is so small that you could not be injured by en electrical shock during the brief period it takes for the breaker to trip. In this way a malfunction cannot present a danger of electrocution even if you are holding the device when it happens.
There is a less-significant factor from a safety standpoint, but significant for proper function of certain types of devices. If the exterior of the device's case is Grounded, it becomes a very effective barrier to penetration of electromagnetic noise signals from outside, and also a limiter on how much noise from inside the case will be broadcast out to the surroundings.
A GFCI works in a very different manner, and it works with NO Ground if none is available. Now, any GFCI WILL have a third Ground terminal and hole, and it really ought to be used with a Grounded cable supply so you have the Ground function, too. But even without that, the GFCI function will work. What a GFCI unit does is constantly compare the currents flowing through the Hot and Neutral lines to the device plugged into it. In any proper circuit operation they should be exactly the same - what goes out must come in. BUT if there is an imbalance exceeding some specified limit (I think it may be 5 mA, not sure), it is assumed that current is leaking someplace it should not go - quite possibly into YOU! - and the GFCI trips the circuit off. That is, it disconnects at least the Hot lead so the device plugged in has NO voltage supply from there. A GFCI mounted in an outlet box does not overload the breaker in the panel and trip it. It does NOT provide any true Ground connection to the outer surface / chassis of the device plugged into it. It cannot provide any electrical noise protection. But it can provide protection against most causes of electrical shock to users of the device.
So they operate on different principles. A Grounded outlet guarantees a zero-voltage exposed surface via a safe current conduction path that is sufficient to trip the supply breaker. A GFGI checks for current balance and switches itself off if it thinks there is a leak. Both can prevent accidental electrocution in most cases of equipment malfunction. But since a GFCI mounted in a box with no Ground lead in its supply cable cannot actually provide a Ground, that fixture MUST be labeled as having no Ground so that users are not misguided by making faulty assumptions.
By the way, about assuming a metal box in the wall is Grounded - definitely NOT. It is true that some wiring systems use conduit or BX cable (with the spiral metal casing) that contains only the Hot and Neutral wires, and relies on the metal cable case to be the Ground lead. In those systems the outlet box may well be adequately Grounded, depending on how well the installation was done. But it is much more common in houses with 2-slot outlets to find that the supply cabling does NOT have any Grounding conductor - it is strictly two current carriers and non-conducting insulation. Testing is required to verify whether any Ground is available at an outlet box. Even the test recommended above - place a test lamp from Hot to metal box and see if it lights - is not good enough. In that test you will get a light even if the Ground connection quality is too poor to provide adequate safety. A much more sensitive test is really necessary, and that usually will need a qualified electrician to do.
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