Like lots and batches, serial numbers are properties that can be different for stock items of the same product. If a medical device company is making spinal cages, for example, it may have a specific 30mm spinal cage part with product ID LC30-5, but it may have ten of these parts in stock and each of the ten stock items may have its own serial number.
When creating a purchase order or sales order for a product, you typically wouldn't commit to the specific serial number of the product until you receive or ship it. To continue with the medical device example, you may make a purchase order for five LC30-5 spinal cages, but you don't specify the five serial numbers until you receive the shipment. Similarly if you sold these devices then you wouldn't specify the serial numbers at the time of making a sales order; you would specify them when you make the shipment.
Inventory management software needs to allow you to work generically with stock quantities of a product or specifically with specific serial numbered instances of the the product, depending on the stage of the purchase or sales process.
Examples from Finale Inventory
Here is an example video of using Finale Inventory to keep track of stock items with serial numbers.
Stock items with serial numbers