Can anyone explain in layman's terms, using simple terminology, what exactly is the difference between ISSN and ISBN? There are lots of links on the internet, but they are complicated and use legal terms, and don't explain the difference very well. What is the difference between the two?
The International Standard Book Number (ISBN) identifies a single, nonrecurring publication, such as a novel.
The International Standard Serial Number (ISSN) identifies a serial, recurring publication, such as a monthly journal.
I tried to give the clear and concise answer asked for in the question. But given the other answers and comments, I'd like to clarify some misunderstandings:
The word "book" does not have the same meaning for the publishing industry as for the general public. For a lay person, a book is defined by its appearance, e.g. the number of pages, the binding, and so on. For the book industry, on the other hand, a book is defined as a non-recurring publication.
ISBNs can be assigned not only to what the lay person thinks of as a book, but also to audiobooks, ebooks, maps, software, looseleaf services, and so on.
On the other hand, what looks like a book to the lay person may in fact be an issue from a recurring publication such as a journal or a series of monographs and will carry an ISSN.
Further issues worth mentioning ...
An ISBN is a product identifier, not a book identifier, although the products eligible for ISBN assignment are generally books, or products closely related to books.
The product is usually a single volume book, but a set of three different books sold as a single unit, or a set of ten of the same books sold as a single unit, would have an ISBN assigned even if the individual books had their own ISBNs.
Some other products are eligible for ISBN assignment -- instructional DVDs that are a teaching tool (rather than just documentaries) are eligible for ISBN assignment. Maps, also, and educational or instructional software.
Hyphenation of an ISSN is always XXXX-XXXX because it only has two components and the checksum is not separately hyphenated, but ISBN has four components and a checksum, and hyphenation is very varied: 97X-X-XX-XXXXXX-X or 97X-XXXXX-X-XXX-X, etc.
If individual editions of a journal are available for sale individually then they should be assigned an ISBN, hence the individual products have ISBNs while being members of a series with an ISSN.
It's quite common for the same series to be assigned one ISSN for printed products and one for online products, even if the content is identical.
The master source of information is the ISBN User's Manual from the International ISBN Agency, available in various languages here.
The ISSN manual is here.
Edit: Related to the ISBN and the ISSN are the International Standard Text Code, which is an identifier for text-based works, and the International Standard Name Identifier which is the unique identifier for the public personae for contributors to creative works.
Edit: Another thought -- the ISBN is primarily a tool for tracking and identifying a product through a supply chain. Although various stages in the supply chain might have their own identifiers for a product, the ISBN is the common value that links it from publisher to end consumer (retail or library, mainly) sale. This is why an ISBN is not needed for a book product that does not pass through a supply chain (for example Kindle Direct Publishing or privately published books).
ISBNs are also used to link different products, so metadata on a product might include ISBNs for the previous edition, the next edition, a replacement product, different formats available for the same product, other products in the same series, other products available by the products contributors, etc..