Doesn't sound right. I have tons of free books I got on my N1E that are now on my NST.
My guess is that you somehow bought a different edition of the same book than the one you already owned. How, exactly, did you "download" it to your NST? Did you use the "Shop" function, or was it already showing in your books, waiting to download?
First of all, everything you have on your old Nook should also be in your online library, unless you actually deleted it. Click on "My Nook" at the top of this page and go to your library and verify that the book is there. If it is, you should be able to download it to any other device.
I wonder if there could possibly be a glitch with that particular book? I don't know. I have hundreds of ebooks in my nook library (okay I have 400 ). Most of them I got free when I used my N1E. I did have them all downloaded to my NST (until the last update when I started to run out of room) and I have never been charged for a previously free book to be downloaded. If the book was reissued with a new ISBN it would be treated as a separate book entirely and not linked to the original download.
You're using the same account/email address for both nooks, right? Do I understand right that on the NST you went to the B&N shop to get the book? If you're using the same account then the books should be in the library portion of both your nooks already and you shouldn't need to go to the shop section. If it says download over the cover, you should only have to touch the cover in the library and it should automatically download from your B&N account to the NST.