Analytical testing is the laboratory measurement of a sample’s properties — most centrally here, whether it is the compound it is claimed to be (identity), and how much of the sample is that compound versus anything else detected (purity). It matters because a printed strength or a claimed compound is a statement; a certificate of analysis behind it, from testing actually performed on that lot, is a measurement.
Analytical testing is a distinct discipline from other checks a laboratory can perform on a research material — heavy-metal screening, endotoxin testing, and sterility testing are each their own method, answering their own specific question, and are not interchangeable with an identity or purity result or with each other. A certificate should state plainly which tests were actually performed for a given lot, rather than imply a broader battery of testing occurred.