120.4 - Just for clarification.
CAT III - AutoLand Mandatory. Limits described above but basically 50RA/200m (or 150m if you are an RJ100?) for CAT IIIa, less for 3b (A/C dependant)
CAT II - AutoLand Probable! On our 737 Fleet you can disconnect below DA (100'RA/300m) and manual land, but it is normal to autoland.
No different training for any of these.