Soil strength and soil stiffness are both represented in the SPT results. Remember that changes in moisture content may radically change both strength and stiffness AT THE TIME OF THE TEST. The SPT is a valuable test but, must be used with a good deal more thought than I believe is commonly used.
The problem is to obtain a proper definition of what is being obtained by the test and what is required by the project to be designed.
I oftentimes deal with unsaturated soils, oftentimes dessicated. Very dry alluvial clay my have high SPT, be very stiff and exhibit a lot of strength, IN THAT DESSICATED CONDITION. After development of the site, usually with landscape irrigation, drainage water accumulations and decreased soil moisture evaporation beneath structures and pavements, the soils soften. A new SPT may be radically lower lower, strength is less and the soil is less stiff.
If I am measuring a sand SPT, the change in the strength and 'stiffness' ( actually 'firmness' for granular soils) may not be near as 'radical' as for the clays.
The problem then becoms, is the SPT actually measuring what I need? If I need a saturated clay measurement, the SPT in a dry clay may be only a crude approximation. If I am dealing with soils cemented with a soluable mineral (gypsum), the dry SPT may be very high but, the soils may actually be collapsible (metastable) when saturated. The high SPT is not only useless but, may be dangerous!!
So I repeat ... The problem is to obtain a proper definition of what is being obtained by the test and what is required by the project to be designed.