In the UK, police people usually see themselves as a part of the society that they serve.
In the US , police people often sees themselves as apart from society, in authority over it, including the privilege to use deadly force.
There are guns in the UK, as there are in the US ... not so many, for sure, but the bad guys have them, so let's not think that makes a huge difference.
In the UK a police person would say to you "I am a policeman(woman/officer)".
In the US a police person would say to you "I am police", as if it were a nationality or a tribal identity, rather that a role.
In the UK the police are understood to be a non-military part of an integrated society. Police people are us, in uniform, protecting us and keeping the peace.
In the US the police are understood to be a military force, separate and distinct from 'us' who have authority to enforce the law upon us.
In the ancient world, the Romans saw nature as chaotic and terrifying. To create peace, the natural order had to be vanquished, suppressed and conquered with brute force - or else it would get out of hand. Everything Roman is about domination, enforcement.
By Contrast, the Greek saw nature as complex, manageable, organic. To create peace one lived in harmony with the natural order, coercing, motivating and training it. Everything Greek is about interaction, communication, appreciation.
To be sure, I don't many many police people on America. The ones I do know are wise, kind and gentle people whom I trust. But then again, I live in New Hampshire, which along with Iowa is one of the safest of all the States. To be sure also, the police in the UK are not perfect, and I read of scandals in the 18 years I have lived mainly in the US.
I hope for a sea-change in American society where our police leaders shift from Roman to Greek. I hope to never hear again about law 'enforcement', but about policing of, for and by our society.