Congratulations, SweetKay. These are really cool devices.
Kate, e-books purchased from B&N will only be available for the Nook, and e-books purchased from Amazon will only be available for the Kindle. They will embed some form of Digital Rights Management into the purchased e-book so it can only be read on their device.
As an example, suppose you purchased 20 e-books from B&N to stick on your Nook, and then you decided you liked the Kindle better after someone gifted you one. You couldn’t simply move those 20 e-books over to the Kindle – if you really wanted them on the Kindle you would have to purchase them again.
As long as DRM isn’t present, however, you should be able to read an e-book on a variety of devices. You may need something like the freeware program Calibre in order to convert an e-book to the native format for your device, but this is an easy thing to do.
I can grab free e-books in the EPUB format from Google books and read them directly with my Nook. You can’t do that with the Kindle, but using Calibre it takes just a few moments to convert the e-book to the Kindle format.