Does the epub and paperback publication of same book requires separate following identifiers ?
First, we need to distinguish what is what code is used for. Some code do not describe books (
URN). Others describe library sorting (
DDC), where these systems were built long before computers and electronic books (LCSH - 1898, DDC - 1876). And there is not a complete practice of dealing with this.
ISBN - International Standard Book Number
This is for books. Practice is such that every format (
DjVu etc.) has own ISBN. (It should be.) Sometimes a paperback and a hardcover book have their own ISBN code.
ISSN - International Standard Serial Number
This is for periodicals (magazines, a periodically published series of books etc.) It is not required in my country. Perhaps it will be similar in other countries. What I know, the code should be the same (for paper and digital copy).
ISMN - International Standard Music Number for Printed Music
This is for music. No for ebooks.
URN - Uniform Resource Name
URN uses a "urn" scheme and does not address the availability of the identified resource. This is prefix example for ISBN and ISSN.
LCSH - Library of Congress Subject Headings
I am not American. I do not know how you handle it. I recommend visiting the congress library web site.
DDC - Dewey Decimal Classification or Dewey Decimal System
I suppose it should be taken as another edition of the book. What I know is distinguished by the letter (one character) at the end (in my country). But library practice may vary.
ISBN - different
ISSN - same + postfix
DDC - same + postfix