What exactly do they consider the difference between a "person of interest" and a "suspect?" Do they have different definitions?
They're meaningless. A person might very well be a suspect even tough not openly deemed one. I'd bet anything that Casey was a suspect from day one, and that she was also the only suspect in this case. The term can't be used at her trial. And LE's case isn't any stronger or weaker based upon how it classifies Casey. It means nothing.