When you’re publishing a book through CreateSpace, it gives you four ISBN options:
CreateSpace-Assigned ISBN (FREE)
CreateSpace is both a printing house and a publisher. As such, they have bought a set of one zillion ISBNs from Bowker, and they assign one to your book. Because CreateSpace bought the ISBNs, CreateSpace is the publisher listed. You cannot change this without assigning your book a fresh ISBN.
Custom ISBN ($10)
As in the previous case, CreateSpace takes one of the zillion ISBNs they bought from Bowker and assigns it to your book. As far as Bowker is concerned, because CreateSpace bought the ISBNs, CreateSpace is the publisher. You can’t change the publisher for your book unless you assign it a fresh ISBN.
HOWEVER, CreateSpace makes it appear that you are the publisher by going into Amazon.com and simply replacing their name with yours. Similarly, whenever they sell your book to someone (either to an end customer or for resale), they say that you’re the publisher. However, your ISBN still encodes CreateSpace as the publisher, which is why if you want your book published somewhere else, you can’t take the ISBN with you. CreateSpace is really the publisher, not you, they’ve just made it seem like it’s you by listing your name on their site.
Custom Universal ISBN ($99)
In this case, CreateSpace goes to Bowker and purchases a fresh ISBN in your name, so you are officially listed as the publisher and thus can take the ISBN with you even if you choose to print your book somewhere else.
Note: This option is actually cheaper than buying directly through Bowker if you’re interested in just one ISBN, due to an arrangement CreateSpace has with Bowker.
The final option is for you to provide an ISBN that you’ve purchased through Bowker (or the ISBN Agency for your country). This ISBN encodes you as the publisher, so you can use it no matter where you print your book.
Hope that helps!