The iPad User Guide is free, and you can bookmark it in Safari on your new device: http://help.apple.com/ipad/7/
There's also a (free) PDF version, and if you go iBooks Store, you'll certainly find an ebook - also free - there as well.
I don't have an iPhone, so I can't tell you about the similarities, sorry. Afaik they're different, but not too much. Someone else will have to confirm that, though.
I have both, and the iPad Mini is very similar to the iPhone 5s. I doubt you will need another book. Actually, the best tips and tricks I have found for both have been online... search for that sort of thing - there are many brilliant geeks posting great information for users! Incidentally, the Retina Mini is absolutely wonderful - and most apps run on both the Mini and the 5s. Enjoy!
While the operation of the iPad mini and the iPhone 5S are similar, there are enough differences to make studying the user guide that Johanna provided a link to.