Originally Posted by
JDNSW
Rolling radius of radial tyres does not change measurably over the entire range of practical pressures. It is a misconception that pressure changes the effective radius - unless the tread is slipping on the road, every revolution of the tyre covers the same distance, as the belt behind the tread is essentially incompressible. The actual effective radius is a little less than the apparent radius, as the tread rubber outside the belt is compressible - how big an effect this is depends on the tyre construction and materials and is different for each type of tyre, but the effect is small for any normal tyre. (crossplies are more affected by pressure)
The difference in pressure specified is a compromise between ride, tyre life, and handling, with recommendations changing over time as ideas and priorities change.