As with many things your THINK you know, the reality is NO ONE actually knows the origin of EITHER term. The one thing absolutely certain is that there will ALWAYS be several explanations for both, and some people will sweat to each and every one of them.
Determining the origin of slang terms is difficult sometimes because the origin is lost by the time the slang becomes popular. There is often disagreement between Etymologists (people who study word origins).
Most Etymologists agree the phrase "cop" came from the Latin word "caper" meaning "to capture". The copper badges came later, as did the acronym Constables On Patrol (the called it "watch" back then, not patrol).
Experts don't agree so much on the term pig, but there are three popular theories.
The first comes from around 1600 when the term "pig" was used to describe a generally disliked person. The second comes from around 1940 when George Orwell wrote a book called "Animal Farm" where a pig named Napoleon creates a secret police. The most current is from the 60s when protests were common. The police wore gas masks with a filter that resembled a pig's snout.
參考: Law enforcement since 1991
It comes from the Dictionary of Buckish Slang, University Wit and Pickpocket Eloquence, published in London in 1811. In it says the pigs frisked my panney, and nailed my screws. Meaning that the officers searched my house, and seized my picklocks.
C.O.P. originally stood for "Constable On Patrol" and as far as I know never had anything to do with copper or badges.
The definition of 'PIG' is Pride, Integrity and Guts. I doubt, very much, if police officer badges are made from copper.....this metal is too soft.
More a American term than world wide. They are seen in dumpsters in America behind donut shops at night rooting around after they close for a donut fix.
You "know" nothing. One theory, out of many, as to were cops came from does come from the copper individual numbers that were soldered on to the star that British cops under Sir Peale wore.
As far as pigs starting around the sixteenth century “pig” began being used in English as a derogatory term for people, whether police or not.
I've heard several explanations for the use of the term "pig" for officer
"Pigs at the [public] trough." (police officers living off the taxes imposed on the people while not helping improve society).
Of course the explanation that officers wearing gas masks in the 60's looked like they had pig snouts (I believe this one is closest to the truth). I've even heard that pigs are considered "unclean" animals in some societies and some people considered police officers to be equally unclean.
Another possibility is that pigs in comic books and cartoons tend to have all consuming appetites (basically taking everything around them for themselves) and some people link this behavior to officers writing tickets and "taking" hard earned assets from other people.
the beatle's sgt pepper's lonely hearts club band song, "i am the eggman".