I've seen a few of these over the years but don't know much about them, I drove by a garage today that had one for £5K, which doesn't seem a bad price. Are they a re-bodied 350z?
According to Wikipedia they're a variant of the Infiniti G35 with manual transmission for the Japanese market so yes, it's related to the 350z via the G35.
In a way, yep, they are a rebodied 350Z, they were originally sold as an Infiniti G35 in the US, Nissan also decided to use the car as the vehicle to take the Skyline name and become a more luxury version of the 350Z.