And one more way of explaining this kind of difference without seriously questioning either result: all standardized testing is a sampling from a moment in time of an examinee's skills in the area assessed. All instruments have some level of measurement error, and these are no exception. This is why scores should properly be reported as confidence intervals (typically the 95% c.i., for index scores), to capture the sense of an informed estimate of some idealized "true" score. On the WISC-V, the 95% c.i. for the QRI is a range of about 13 to 14 points, centered around the nominal index score. The WJIII or IV subtest in question also has a confidence interval, which is probably about the same magnitude (I don't have the exact figure in front of me). Taken together, one can see that, based purely on standard error of measurement, a difference between the two scores of roughly this size would not be entirely surprising.
The situation reported by snowgirl, of a difference of multiple standard deviations, is a bit more striking. I'd have to have more detail to take a stab at that.
