In general, current ratings are the current that the device is able to deliver without overheating or throwing a circuit breaker or wasting a fuse. If one of these things happens, then current will be limited as a consequence, but otherwise the idea of current limiting is somewhat curious. The only way in general that current will be limited by any device is if the device is overloaded with current and one of these catastrophic things happens, or else if the voltage output by the device is reduced, such that current is reduced in accordance with Ohm's law and in accordance with the impedance of the device to which current is being supplied. In the particular case of current supplied by an amplifier, the amplifier may employ circuitry that will automatically reduce the gain in the event that current is excessive, and possibly in the event that voltage peaks come near to the clipping threshold. When/if an amplifier automatically reduces gain in response to one of these circumstances, there will be a reduction in current commensurate with the reduction in output voltage. Simple devices that deliver AC power, i.e., power cords and similar, do not have gain and do not generally have a smart method for reducing the voltage they output. As such, if simple devices such as power cords or power strips limit or reduce current, it is either because one of the aforementioned catastrophic events has occurred, or else because the voltage they output is reduced in accordance with the voltage dividing effect. The voltage dividing effect occurs when/if the internal impedance of the device supplying current is great enough to be significant in comparison with the impedance of the device to which current is being supplied, such that a significant portion of the voltage nominally output by the device supplying current is taken up within that device.
A perfect illustration of this is what happens with batteries generally, as they age. As they age, the internal resistance increases, such that a greater portion of the voltage nominally generated within the battery is taken up within the battery. The increase in total series impedance means that current is reduced. The reduction in current requires, again in accordance with Ohm's law, that there be a reduction in voltage seen by the device being powered by the battery, i.e., a reduction in voltage across the battery terminals. From the standpoint of the voltage dividing effect, the increase in the battery's internal resistance implies that the impedance of the device powered by the battery decreases proportionally, i.e., as a proportion of the total series impedance. This decrease in the powered device's proportional share of the total series impedance implies a corresponding decrease in its proportional share of the nominal voltage generated within the battery. Thus, the battery supplies less current than it did when it was young and vigorous, but this reduction in current occurs in perfect conjunction with a reduction in voltage output by the battery, and the reduction in current could not possibly occur except in conjunction with the reduction in output voltage.
(I should probably note, at the risk of complicating this more than I already have, that if you measure the voltage supplied by a battery when the circuit is open, that no matter how great the internal resistance of the battery, it will be very small in comparison to the near-infinite impedance across the terminals, which means that essentially all of the battery's internally generated voltage will appear across the terminals, giving the false impression of a good battery even for a battery that has already kicked the bucket in practical terms. To check a battery, you can check either current or voltage, but either way, you have to do it while the battery is being asked to supply as much current as it needs to be able to supply when in use. Since voltage readings are usually simpler than current readings with an ammeter - which generally involves a shunt - the easier way to check a battery is by checking to see whether the voltage it supplies to the normal load for the battery is the same or very nearly the same as the voltage supplied to that same normal load by a new or fully charged battery. Of course this has very little relevance to what I wanted to say about the concept of current limiting, but after I had said what I wanted to say, I decided that I had better say this as well, to tie up the loose end.)
