LAPD changed their IDs about 4 or so years ago. Not much like the classic ones, and they are now in a vertical design. Badges and ID's just gave / give rank but not level (Detective, but not Detective I, II, etc. and Officer includes SLO rank).
For old Joe Friday (Webb) his ID card and badge said Sergeant although he was assigned to a detective division. For a while he was a lieutenant (I have his card and badge from that). For the 2003 version, if the shield said detective, I'd go with detective on the ID.
Incidentally, I particularly liked Ed O'Neil's portrayal of an NYPD detective in "Big Apple."
As an aside, when departments went toward a smart card design, many were unpopular with the members. In some instances, cops kept their old fashioned ID cards because they looked more "official" and put the new ID cards behind the old one. So will you see old style LAPD, SFPD, etc. cards used by officers? Yes.