No the 'IdentifyingNumber' is the Serial Number.
Every HP product has a product code that identifies that particular model and specification. For example we have HP Probook 4530s with product codes:
XX992EA - Intel Core i3-2310M 2100Mhz, 3Gb Memory, 300Gb Hard Drive
A6E08EA - Intel Core i5-2450M 2500Mhz, 4Gb Memory, 600Gb Hard Drive
B0W44ES - Intel Core i3-2350M 2300Mhz, 4Gb Memory, 500Gb Hard Drive
So basically from the product code you can identify the hardware (processor, memory, harddrive, etc) and build of the machine, as machines with the same product code will be actually the same.
Steve