Why New Zealand Sauvignon Blanc and French one are so different? Why New Zealand Sauvignon Blanc and French one are so different?
Like they would be two different grapes..

And this difference is stable. Or may be this is false and there are French Sauvignon Blanc that tastes as New Zeland and vice versa?
The French call it “terroir.” Microclimate, soil composition, even water minerality all have an effect on how the grapes taste. 

Then there are the style elements, often dictated by tradition (and law, more below). How long do the grape skins remain in contact with the grape juice? How long is the wine aged? What is it aged in (stainless steel tanks vs barrels, etc). 

Back to the tradition piece, France and many other European countries have laws and a legal designation system applied to their products. You may have seen them: Appecation d’Origine Controlee (AOC), Vin de Pays, Vin Ordinaire, etc. 

All of those factors play into whether you can get the coveted AOC, which requires strict traditionalism. You can sell your wine for a lot more with that designation. More experimental things will get you a lower tier certification.

Newer/non-EU wine-making areas (Australia, New Zealand, Chile, USA) have no such laws, and are free to experiment.

Couple the terroir with the lack of homogeneity,  you have lots of room for difference.