Accepted answer
What a useful certificate carries is debatable, but there are certain fields that almost no research-grade certificate includes despite their being standard in pharmaceutical work.
The laboratory name and accreditation status can be checked in real time against the testing service's own register, and that two-minute check catches substituted certificates.
In practice, comparison across certificates from different laboratories is almost never valid, even when the material is the same, because the methods are almost never the same.
Industry guidance on this topic is consistent because it comes from first principles rather than convention.
The practical summary: check the lot number, ask for the method, and reserve judgement until you have both.