I have several books that only have ISBN-10, no ISBN-13.  I find matches on the ISBN-10, but the existing entries also have ISBN-13 listed.  The covers are also different (I know that doesn't necessarily matter).  Do I need to create new entries for my copies that do not have ISBN-13s?

The ISBN 13 is newer than the ISBN 10.  Usually the last digit is different.  Maybe the last few. If the ISBN 10, the title, author and binding match than you can post it w/o it having an ISBN 13 on the book. Some books will only have the ISBN 13 on them and some will only have the ISBN 10. 

As Mary said....and

In January 2007, publishers started using  13 digit ISBNs, and the 10 digit would still be used.  Publishers were encouraged to print both the 13 and 10 digit ISBN on the back of all books.   Read more here.

Here is a conversion tool to convert 10 digit ISBN to 13 digit ISBN

What Mary said

Thanks for the answers

For the sake of clarity, as long as the ISBN-10 matches (and the title, author and binding, of course), you're fine, Thad.