The simple and only difference is:
300zx are sold in USA.
Fairlady Z are not.
There are two different types of markets. And also two different type of emission standards to be met. Hence the reason why we can by low mile JDM motors, and why JDM tuners have rich access to those cars. And finally, Nissan had to play nice with Toyota and Honda, with their gentlemen's agreement which all agreed to limit their advertised power in Japan.
Mr. Katayama, recognized early on that Nissan could not use the same business strategy used in Japan. Also he had a renowned fear of driving on the freeway with Datsun cars, they were too slow. That's why the older cars were fit with more powerful engines to catch up with the American cars.
In the end. All parts are interchangeable. The Japanese cars had yellow mark pieces that they could remove to attain the more power potential figures.
There are many cars that have interchangeable names/brands in the in global market.
For starters:
G35 and G37 is a Skyline
Anyways, congrats. You appear to own a legit Fairlady Z.
And socially the only difference in USA for titling your Z32 is being called "cool" or "dork". Let me elaborate..
"hey man, what kind of car is that?"
"Oh it's a Fairlady Z"
"What's that?"
"The car from Japan, that's their name for our 300zx"
"cool"
verses
"Oh I rebadged my 300zx to a Fairlady Z because that's what they have over there in Japan"
"Dork"