Thanks for the clarification, seems boeing uses the same indication for different purposes in different models.
By the way, fail passive CAT III is the standard equipment on the 737, you can order fail operational CAT IIIb which then sports the nice LAND 3 and LAND 2 indication as the other boeing aircraft. Fail operational is then done with 2 autopilots only and LAND 2 simply means you are on fail passive status and due to fail passive operation you have to use higher minima (50ft 125m RVR instead 0/75), rollout is still available though. Single engine will usually give LAND 3 status, however due to certification only CAT IIIa minima are usable.
Reason for the 50ft minimum during fail passive operation is the ability to still successfully initiate and fly a go around with any failure down to minimum and land with visual cues below that. During fail operational you do not need that as any single failure below AH (200ft, land or go-around decision taken there) still allows a successful autoland.
LAND 3 fail operational -> 0ft/75m
LAND 2 fail passive -> 50ft/125m
NO AUTOLAND -> CAT I.