I know many things to do with publishing seem alien and acronyms don't help. Well, let me demystify these two.
ISBN: International Standard Book Number. Not to be mistaken for copyrighting this is a number assigned to your book to make it easier to sell and buy. It used to be 10 numbers but about ten years ago they moved to 13. Probably because there were too many books and you can't reuse numbers if the book is still in circulation. This was invented ages ago by a company that knew a really clever way to make money for nothing. You don't get anything for your money except the ability to sell your book all around the world. If you live in New Zealand you are lucky enough to be able to get your ISBN from the National Library.
Once your ISBN has been assigned you can't change the product. You can change the cover as that is advertising and you can fix typos but if you are changing scenes and taking out whole chapters you will need to get a new ISBN. You can't change author name, format, size or title either. I knew a clever author who had their old name in small and their new name massive with a little AKA on it. A great way to change things without changing anything.
You will also need a separate ISBN for each format.
ASIN: This is unique to Amazon. The clever guys realised why deal with ISBNs when they could cash in on their own. Amazon doesn't charge you for an ASIN but you also don't need an ISBN if you are publishing on Amazon alone. I often will only get an ISBN for my print and use an ASIN for my digital version. I sometimes will get another one for Epub so I can publish on Smashwords.
There is a lot of argument over whether you need ISBNs for all the formats especially the digital versions. At the moment, the powers that be have decided you need separate ISBN's for all the formats.