As an example of what I'm talking about, here are two "shield" type badges:
And here are two "star" type badges:
Then there are some that seem to blend the two, like this NYPD badge from 1972, which interestingly is a "Police Woman" badge. There are many more exampls of different styles of NYPD badges on this page.
I personally associated the star type of badge with the stereotypical Old West and Western states in general, but I have no idea if that has a basis in reality and those NYPD badges show that they've been used in other parts of the country. And I found examples of shield type badges in many Western states as well.
Where did these two styles come from and how have they changed in use and popularity over time? Have there been fashion trends in police badges?
On that note, why are some highway signs in Canada and the US in the shape of a shield?
Just a heads-up: Your link to the 1972 badge is broken due to an accidental "]" in the URL.
http://copspassions.pagesperso-orange.fr/NYPD%20badge%20Woman%20%28YD%29.jpg
I think the badge or shield goes back to the Roman era where the soldiers carried and actual shield with their unique signature that gave them the right to enforce the laws of the Empire.
The star is somewhat the same but it originates from the English common law.The Sheriff who was in charge of the county and the protection of the King's Peace, carried a star(symbol of a watchman) representing his authority given by the king.
Back then only authorities carried shields and swords. Today the shield has become a symbol and also an identifier, and the sword became a gun.