Sorry, I was trying to keep it short, but wound up being confusing instead! 
CAT I approaches are almost always Baro, and use a Decision Altitude.
CAT II approaches are mostly Radio, and use a Decision Height.
The reason I qualify those is because the FAA leaves words like “typically” in their documentation and I seem to recall at least a CAT II that used Baro…though I don’t recall where.
CAT III, AFAIK, are always Radio with either a Decision Height or an Alert Height.
Again, generally speaking, it goes like this:
CAT III with a Fail Passive autopilot is allowed a DH, usually 50ft, where the pilot must see the landing environment to land.
CAT III with a Fail Operational autopilot is allowed an AH, usually 100ft, where the pilot must only verify electronically that the aircraft is set to land in the landing zone.
That’s a very basic description with a lot of “ifs” and “provideds” in there. 
BTW, the 320 only requires you to enter the AH/DH/DA on the Perf page (I think it is, the 320 has prog stuff on the perf page and vice versa, it’s easier to find than describe!) in either the BARO or RADIO fields.
It sounds like you need to manually set some of this stuff in the 310.