Hello Bruce and welcome to the forum,
You ask some very good questions. The differences in using most of the probes is really in accuracy. For a planer material, the concentric ring electrode is the most accurate. However, it does require a somewhat large sample size with a flat surface. It does have its limitations. If the material is not homogenous, the most conductive path may be the only one that is being measured.
The two 5 lb electrodes will measure point to point but is not typically used for surface resistance. These are used for worksurfaces and floors and will take into account multilayer constructions. If the materials are homogenous, then the ring electrode and 5 lb electrodes will be similar.
The two point probe is used when there structures are to small to use the ring electrode. If a material is not homogenous, then measurements can be significantly different between the ring electrode and the two point probe and different with the two point probe in different places on the material.
With that information, you can look at ANSI/ESD S20.20 for which method should be used for qualification. For worksurfaces, floors, garments and most ESD control items, the 5 lb electrodes are used. For packaging materials, the ring electrode is used. One reason for that is that the 5 lb electrodes are limited for the high resistance measurements that packaging uses.
The two point probe can be used in ANSI/ESD S541 along with the ring electrode for packaging material. For small structures there is no choice but to use the two point probe needs to be used.
For which one is correct or to be used for qualification, instead of comparing the measurements, see if the measurements meet the qualification limits. The limits are very broad and instead of comparing one measurement to the other, if both are within the qualification limits then the material can be considered qualified.
Please post any additional questions if you like.