Hue shift, absolute replace, colourise
The mode decides more about how a recolour looks than any tolerance does. On a photographed surface one of them keeps the material and one turns it into paint.
What each mode writes
Hue shift rotates each selected pixel onto the target hue, scales its chroma by one factor and leaves its lightness alone. Absolute replace writes the target colour, varied only by each pixel's lightness relative to the selection's mean. Colourise ignores the sample: every visible pixel keeps its lightness and takes the target's colour.