Your customer orders by their code, your supplier invoices by theirs. Item References translate both so nobody retypes.
On the item card, Item References (formerly cross references): add a line per customer, vendor or barcode with their number and optional description and unit of measure. On a sales line, type the customer's reference in the Item Reference No. field and the item is found; the customer's number prints on the confirmation and invoice. On a purchase line, the vendor's number likewise, and it prints on the PO. Barcode references are what scanners resolve.
EDI and web shop integrations rely on these; set them up before go-live, from the customer's and supplier's lists, and the "wrong item shipped" tickets drop. The item card also has a field for the vendor's item number for the main supplier; references cover the rest.