Collecting this in one place because it comes up every few weeks and the answer is always assembled from scratch. 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
Mass spec answers a question purity does not: identity. High purity tells you one thing dominates the chromatogram, not that it is the molecule you ordered. A mass within about a dalton of expected is the identity check.
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
The bit I cannot resolve on my own is why two laboratories report different purity for the same batch, and which number to believe. Happy to be told the question itself is wrong.
— SaraMom3 · corrections welcome and will be edited into this post with credit