Differences between the oven stone and the pizza oven?
A pizza stone in a normal oven will only get the maximum temperature of the oven (probably not more than 280 ºC / 530 ºF).

A specific pizza oven will gett hotter (the one you linked gets 390 ºC / 735 ºF and, indeed has a stone inside).

If you want to get Italian style pizzas, go for the pizza oven. They need that high temperature in order to be ready in (ideally) 90 seconds. Those Ferrari ovens are one of Italian's favourite ones, albeit they'll need a bit more time than 1.5 minutes achievable in wood fired traditional pizza ovens. 

You (probably) won't be able to achieve those high temperatures with a normal home kitchen oven, unless you have a pyrolytic home oven, and hack it in order to cook in it during the pyrolysis cycle.



As for the waiting time between pizzas using a stone, consider it as a capacitor (or a rechargeable battery): It takes heat (until is soaked up), and then gives it back. Once you make 1 pizza (or a loaf of bread), it needs to soak (a bit) again.