Good to know, Birna ! Thanks.
To be honest, I didn't know they were 2 different mounts.
The internal S-mount for the 5cm/50mm normal lenses was a heritage from the Contax camera. This allowed the lenses to be very compact as they had no helicoid of their own. You focused them using the internal helicoid of the camera. For shorter or longer focal lengths there was an external S-mount.
Here are examples of two Nikkor normal lenses 5cm f/1.4 (late '50s) and the reborn 50mm f/1.4 Millennium (a refined version of the 'Olympic' model from 1964), plus the Voiugtländer 50mm f/1.5 Nokton (ca 2000). The latter uses the external mount and thus has its own helicoid for focussing.
The adapter for Nikkor-S (external) to Z can be found easily, although not all have the accuracy to bring the lens to infinity. The focusing adapters are quite rare yet do exist. One shown here is actually a makeshift one purchased from eBay and turned out to be a clever hybrid between a Leica L-Nikon Z and a hacked helicoid probably from a Russian clone of the Contax. The other is my own remake of the Amadeo focussing mount for Nikkor rangefinder normals to Sony E, which I managed to recast with a factory Z bayonet to be Nikkor S to Z. I reserve it for the 50mm Millennium Nikkor.