The OEM (and airlines) I worked for had a completely different definition for AOG than I have read here:
AOG means: an "in service" aircraft had a problem and is now "out of service" awaiting the spare part.
Airlines could (and did) not order spares as AOG when an aircraft was "in scheduled maintenance" or "late out of a check".
If we got an AOG order for a spare part, we guaranteed that, if the part was in stock at our facility, at a supplier facility or at one of the remote locations world wide where we stored spares, it would be shipped within 24 hours. AOG orders carried a 10% handling fee above the shelf price.