This is the version of the explanation I wish somebody had given me, written down before I forget what confused me. It is about certificates of analysis, and it is deliberately narrow — everything I am not confident about is marked as such.
What is actually established
They are not contradictory, they measure different things, and this is the single most common misreading of a certificate. Purity is a relative area measurement: the main peak as a percentage of total peak area in the chromatogram. Content is an absolute mass measurement against a reference standard. A vial can be 99% pure and contain 6.1mg — pure material, overfilled — or 99% pure and contain 3mg, which is pure material and a short fill. Purity tells you what fraction of what is there is the right molecule; content tells you how much of it there is. You need both, and a certificate with only purity is telling you half the story.
The condition it depends on
One addition: an unstated method makes a report close to uninterpretable. "99% pure" without the technique, the standard and the conditions is a claim, not a measurement.
The practical version
The four things to check on any report, in order: does it name your batch, who commissioned it, what method was used, and does it report content as well as purity. A report failing any of those is weak evidence regardless of the percentage on it.
What I am not sure about
So the question, as narrowly as I can put it: why two laboratories report different purity for the same batch, and which number to believe. Not looking for reassurance. Looking for the part I have got wrong.
— marco_milano · corrections welcome and will be edited into this post with credit