Look, we all know postdocs (postdoctoral scholars, postdoctoral researchers, postdoctoral fellows, etc) are in their temporary poorly-paid positions because the academic pipeline is broken - and not because more training (and certainly not more training in science, as opposed to management, administration, and grant-writing) is actually necessary for them to be qualified. A generation ago, people got their PhDs and then got faculty jobs right away. Now...there is a huge glut, so take a number and get on line and hope for a Science or Nature paper to bump you ahead.
Postdocs have earned doctorates - the highest degree available - and now they are just hanging out in academic purgatory. It's true that some use this time to broaden their skills, but given the ultra-specialization of most universities, that strategy is a gamble. Most just hunker down doing something almost identifical to their PhD work. Anyway, it is just adding insult to injury to call them "students," as though they are working toward any goal, degree, or professional certification beyond getting a job.
Geez, it's been getting on five years since I was a postdoc myself, and when I hear "postdoctoral students" it still drives me apeshit.