Adress book is not an app, its just something you copy your contacts to and from the iphone to the computer. Im on a windows machine and its labeled windows contacts, so on a Mac its probably called something different.
But when you plug your iphone to itunes click on the iphone on the left and then on the tabs in front of you go to "Info"
Sync contacts with:
And select whatever option you want.
You can copy and transfer them using itunes instead of just by using a backup to restore to.