BobSmith54...I see that you are listed in "Geotechnical" so let's use a geotechnical analogy. The compressive strength test is an unconfined compression test (confining pressure=0). With uniform specimen fabrication and generally homogenous conditions, a "double cone" failure pattern would be expected for a triaxial stress state. To receive any other failure mode implies a deviation from a consistent stress state inside the sample. That deviation can come from a variety of sources as there are many variables in the process. As an example, lets assume that the specimen has a high water-cement ratio and a high entrained air content. Voids will result from these two conditions and will manifest in different locations depending upon the rodding process while fabricating the specimen. Variations in the size, quantity, and grouping of these voids will create a "discontinuity" in the homogeneity assumption. Internally, that will create stress raisers and variations in the stress distribution resulting in the various failure descriptions promulgated in the ASTM standards.
Most of these variations (while still achieving some variant on the cone shape) are minor and the end result is an insignificant effect on the macro-strength. As the failure mode deviates more from the cone, the significance becomes greater, leading to an appearance of erratic strength. These can be caused by internal physical specimen variations (voids, aggregate distribution, microcracking, etc.), variations in moisture content through the specimen during curing, variation in load application speed, variations in load distribution at the top and bottom of the specimen and others.
Achieving the "double cone" failure shape is a good indication of procedure consistency in making the specimen, curing, and testing. That leaves only variations in the actual strength of the concrete to explain differences in the observed strength values.