As the author, you have all copyrights to your new work as long as none of it was plagiarized.
But you, as the copyright owner, can assign partial rights of publication to others. For example, you could give the right to publish print copies of your work to a print publisher in exchange for a royalty on each copy. This right to print would be limited only to printed copies and would not include other media formats like electronic forms (ebooks).
"Digital publishing rights", like print publishing rights, is just another division. In this case it covers the right to distribute the work electronically as a digital file or data stream (in essense, an ebook). But, just like the print publishing rights does not include the digital publishing rights, the digital publishing rights does not include the print publishing rights.
Bear in mind that these divisions are purely artificial. You can divide publishing rights for your work any way you like and assign them any way you like. You own them all (unless you sell part or all of them). If you want, you can assign all of your rights to a single publisher and they can distribute your work any way they want. Or you can limit their rights to just one medium. You can even limit their rights to a geographical region (although this is increasingly impractical in today's global economy).
In summary, a copyright owner can divide publishing rights and assign them individually. To publish an ebook, the publisher must have "digital publishing rights". To publish a print book, the publisher must have "print publishing rights". And so on.
Thank you this was very helpful. Finally something that made sense. Now I know I own the copy and publishing rights to my book. I have been searching for hours to find out. Nothing I read was clear. One question, If I die does my family own the rights? Even without the copyright being registered?
As far as leaving rights to your family, they are assets just the way a small business would be. You do need an executor who understands what they are and that some tending will be necessary. Kristine Kathryn Rusch has some really good posts on this issue (www.kriswrites.com).