txinvestigator1 has, as usual, made an excellent attempt at trying offer insight to the generally accepted application of this term in the world of law enforcement.
The only thoughts I can add to this, as an example, is that a portion of the Texas Code of Criminal Procedure (CCP) defines the differences between "Peace Officers" and "Federal Agents." Federal "agents" primarily enforce federal laws whereas "peace officers" primarily enforce state and local laws. There is, at least in Texas, a defined dividing line between the two and what their recognized resepective authorities are. I think this may be a factor in reference to this issue.
I would also add that geographic location lends an effect to the application of this term. What we may refer to as a "COP" in Texas may not be the same as what this term is applied to in some other state.
Charlie
"Good and evil are present in this world, and between the two there can be no compromise" - President George W. Bush, in his farewell address to the nation.