Greetins,
You have to segregate approach category CAT I CAT II CAT III A CAT III B with autoland capability, they are 2 separate things.
CAT I CAT II usualy performed on Auto Pilot then they are followed with a Manual LANDING.
CAT III A ( which is can be viewed as an improved CA II or a degraded CAT IIIB) usualy performed on Auto Pilot which includes an autoland.
CAT IIIB is full auto land.
BTW I flew to Almaty from Seoul in 1997, Freezing fog viz 50 meters, I had to hold for 2 hours to have CAT II minima amd land
