Long and short your question is that they are actually both ISBNs. One of them is in ten-digit format, and the other is in 13-bit format.
978 074942349 0 074942349 8
978 is the prefix, and the last digit is on the check digit. The barcode of the object you are viewing is in only 13-digit format.
According to http://www.isbn.org/standards/home/isbn/transition.asp you can always convert from a 13-digit ISBN, starting from 978 to a 10-digit format and provides a link to an online converter. It also discusses the prefix 979. I do not believe that the prefix 979 is used, but it is good to know that they can be used in the future.
Having worked in the library application space, when searching the library directory, the entries for the elements will vary greatly in the information that they contain. Records of items, in particular with respect to ISBNs, may contain 10-digit ISBN, 13-digit ISBN, both or none. Therefore, to find an item, you may have to try both formats. I believe that some systems, if your search type is set to ISBN, will actually check the submitted ISBN and automatically search for both formats.
Depending on what you are trying to do. Many library search functions allow you to use wildcards, which can make it easier to find the item you are looking for. For instance:
'if the isbn has a length of 13 and starts with 978 remove the first 3 (the 978) and last digit (the check digit) add a wildcard character to the front and back begin search end if
for example, 9780749423490 will become * 07494234 * The disadvantage is that it can return multiple results. Even if this happens, most likely it will be only a couple of objects, and one of yours if there, it would be easy to notice.
As provided by others, the Wikipedia article on ISBN contains more detailed technical information on how to convert between 10 and 13 digit formats. http://en.wikipedia.org/wiki/International_Standard_Book_Number