A student scores 85 on a test with mean 70 and SD 5, and 130 on a test with mean 100 and SD 15. Both are z = 3. Why does converting to z-scores let you compare performances on tests with nothing in common?

C. Because a z-score reports position relative to its own spread.

A z-score asks one question — how far from this distribution's mean, in this distribution's own standard deviations — and that question can be put to any distribution. What makes the comparison possible is precisely that the units are discarded. The caution is about interpretation: a z of 3 in spelling and in the high jump are both 'unusually good for that distribution', and nothing more.