As I understand it "Detective Sergeant" is not, a rank as such. The rank is "Sergeant" and the prefix Detective is a mere designation. Can't understand why PS is used on this particular medal, as you suggest, "Sergt" is usually the norm.
In several forces the prefix "Police" in respect of ranks is regarded as being a total "non, no". PSNI (and the old RUC) is one such force and another is Merseyside Police where the title Constable is used and not prefixed by "Police". The term PS is also very much a "no, no" in Merseyside (and the PSNI). The term "PS" is, in effect, an afterthought on a piece of written correspondence, a fact of which I was forcefully remined of when I had the temerity to refer to a Sergeant as such on my return from District Training Centre many years ago.
Finally, you will never find the term "Police Constable" mentioned in any UK Act of Parliament. You will find "Constable", but it is never proceeded with the word "Police".
Dave.