How are landing minimums decided?
The terms you are looking for are Decision Altitude (DA) and Decision Height (DH). If no visual reference to the runway is established at the DA or DH, a missed approach has to be initiated. So based on the weather and the certification of the airport (CAT I / CAT II / CAT III), the pilot will make the decision to land or not land at the DA/DH.

(Image Source: SKYbrary)

Decision altitude (DA) is referenced to mean sea level and decision height (DH) is referenced to the threshold elevation.
The DH for Category II and III approaches is invariably assessed by reference to a radio altimeter and never a barometric altimeter; therefore the minima can only be expressed as DH and not DA. For approaches with DH of 200ft or higher, radio altimeter reading would be unreliable due to the unevenness of the terrain; therfore a barometric altimeter is always used and the minima may be expressed as DH or DA.
The required visual reference means that section of the visual aids or of the approach area which should have been in view for sufficient time for the pilot to have made an assessment of the aircraft position and rate of change of position, in relation to the desired flight path. In Category III operations, the required visual reference is that specified for the particular procedure and operation.
For convenience where both expressions are used they may be written in the form &quot;decision altitude/height&quot; and abbreviated &quot;DA/H&quot;

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