Yes, they used a test designed to find a difference between two groups, and it failed to report a difference. Your analysis of that is correct, although the te

Yes, they used a test designed to find a difference between two groups, and it failed to report a difference. Your analysis of that is correct, although the terminology "p-test" to describe "a statistical test designed to find a difference" is not. I don't know the general term for this class of tests. The definition of p-values is a bit wonky (there's actually a set of null hypotheses rather than a single one, and it involves a supremum over that set), but the line "if we're wrong, then the chance of seeing this data is at most p" is pretty accurate. All kinds of frequentist statistical tests use them, including equivalence tests.