Those "model numbers" are actually "family" numbers which are not specific enough to identify the finer differences between models. Some of those "Axxxx" numbers may belong to a line of Macs covering six years with many different hardware specifications. Ideally it would be nice if those numbers actually did identify specific models, but they do not.
If your Mac does not boot, then you can use the system serial number found somewhere on the outside of the Mac to identify the exact model by entering the serial number here:
https://checkcoverage.apple.com/
If you have an older model Apple laptop with a removable battery, then the system serial number may be found inside the battery bay or perhaps the memory bay.
For your own Apple products, then perhaps you should write down the exact model while the product is still functioning.