No, sick passenger is code for “dead customer ON the train”. Often times it actually IS a sick passenger though - sick usually refers to some kind of bodily injury, rather than someone puking or passing out, and the delays are mainly from the MTA doing an investigation to cover their asses when that customer eventually files a lawsuit.
“Police investigation” is the code for a suicide by train. Service will be disrupted for about a half hour, usually. I’ve seen it mess up things for as long as 3 hours though.