No, it is not the case, just look at your handbook and buy the standard spec oil recommended in there for the diff.
Some of the six speed gearboxes can obtain an improvement to the gear change if you use Redline MT90 or Castrol Syntrans Multivehilce 75/90. Buy three bottles of whatever gearbox oil you chose as the box takes more than 2 litres of oil.
Do not use either of these two specific oils in the diff.
+1 for the Castrol Syntrans Multivehicle. I was slightly sceptical TBH but it’s made a noticeable improvement to the smoothness of gearchange on my NC 2.0.
It’s quite expensive IMO but definitely worth it. Best price I found was Demon Tweaks on Ebay.