Alex, using ISBN numbers is not mandatory at all, but it is more than advised. It is the unique identifyer of a book and helps working together with booksellers, libraries, universities, wholesalers and distributors.
Yes, it is best practice to have different ISBNs for the paperback and ebook versions.
Maybe these sites help you to get a better insight (and answer the "says who?"):
http://www.isbn-international.org/ and
http://www.isbn.org/standards/home/index.html