One word (category) different meaning and context.
For manufacturing certification purposes an aircraft will only fit into one approach speed category based on (already noted) 1.3 times the stall speed in the landing configuration at maximum gross landing weight.
Now place ourselves in the cockpit flying the Boeing 737-800 after a maximum weight takeoff and we need to return for landing under instrument conditions on one engine and no flaps or we need to divert to a nearby alternate and must to circle to landing (not our day; the engine failure damaged and jammed the flaps) and somebody asks “What category minimums do we use?” It is the same word, category, but now this becomes a practical application issue. We are going to use the approach category for the speed we are actually flying and not the Category C minimums the aircraft was certified as. We are having a different discussion and no longer talking about certification. [For the sake of brevity I am skipping the discussion related declaring an emergency and doing what necessary to land safely and no longer being bound by the “regulations”].
There may be a case where an operator may further limit themselves and require their crews to use the more restrictive minimums say Category D at a particular airport. This now becomes company policy and dispatch decision and not a certification nor a practical application issue.
When this question comes up we need to clarify what context we are discussing approach categories. Are we discussing approach categories in relation to manufacturing certification, line flying application under different circumstances or self imposed operational company policy and dispatch requirements? It is possible to have different answers and each is correct.
For certification purposes our -800s are Category C.