A product key, also known as a software key, serial key or activation key, is a specific software-based key for a computer program. It certifies that the copy of the program is original.
Product key on a Proof of License Certificate of Authenticity for Windows Vista Home Premium
A serial number is a unique identifier used to uniquely identify an item, and is usually assigned incrementally or sequentially.
Traveller's cheques, a kind of insured cash money in form of a paper cheque, are sold to customers in sets having consecutive numbers - one of the very few type of items where consumers have access to "serialized" similar things.
Serial number on a semi-automatic pistol
Serial number of a laptop computer
The RAF serial (XG900) on the Short SC.1