Would I need a WiFi shield?Is that different than in internet shield? It seems the Arduino FIO is wireless capable (wireless ready?).
A WiFi shield is just like a WiFi card in your PC or iPhone. It allows you to connect to an existing WiFi router.It is different from an Ethernet shield. The Ethernet shield requires a wired connection to a router.
The wired/wireless network does not have to be connected to the internet. It can be strictly a local area network.
Somewhere in the picture, you need a WiFi router, for the iPhone to connect to, since the WiFi shield is not a WiFi router.