In either case, "don't do the crime if you can't do the time..."

So my younger daughter balked when I said that I wasn't a big fan of murder mysteries. 

"What?!," she said, "but you LOVE Law and Order."

And that's true, I do love the Law and Order (only, it should be known, the original series -- no matter the cast -- and not SUV, CI, LA or any other combination of acronymic subtitles).  But, as I told her, Law and Order is a cop and lawyer show combined not a murder-mystery, i.e., it's more about the official process of bringing a criminal to justice than it is about finding the murderer.  It's got public officials, not private and/or amateur sleuths, doing the investigating.

So then I got to thinking about popular television shows and how they fall within this spectrum:

Kojak     Cop Show

Adam 12     Cop Show

Dragnet     Cop Show

Cagney and Lacey     Cop Show

Police Woman     Cop Show

Hill Street Blues     Cop Show

Murder She Wrote     Murder Mystery

Matlock , Quincy, and Barnaby Jones are all Murder Mysteries because none of them, as lawyer, medical examiner, or RETIRED P.I., should ever have been in danger of getting offed by the bad guy.

McMillan and Wife     Murder Mystery because even though he was the Chief of Police, they were a mystery-solving duo not unlike the Harts of Hart to Hart.

McCloud     Murder Mystery because, even though he is a police detective (albeit on loan to NYC from Texas), he's unorthodox and is getting into as much trouble with the higher-ups as those hippy Italian-American detectives Barretta, Toma, and the short-lived television incarnation of Serpico did!  In short they're really no different than the private dicks, like...

Mannix     Who the hell cares if it's an m.m. or a cop show?  Joe Mannix was just so cool you wanted not just to watch Mannix, you wanted to BE Mannix!

Rockford Files     See Mannix.

Columbo is the truly odd duck in this discussion (as would be the far-less-effective Law and Order: Criminal Intent) since the show, which is about a police detective, is not really about the murder at all, since the good detective usually figures out the identity of the culprit early on in any episode (and we the viewers then know who too), it's then just a question of how he knows what he knows.

We won't comment on the current trend of "psychic" detectives (e.g. Mentalist, Medium, or the one with the redhead with the photographic memory) since that's just cheatin.'

And Randy Newman's Cop Rock, well, Cop Rock was just brilliant!