Another slight difference is we generally only have 1 police force per state. You can transfer between different stations/areas - but they are all under control of a single state body. If you stuff up badly enough to get fired from one - you can't transfer. You could theoretically go to a different state - but you'd need to declare any past history and if it's bad you won't get a job there either.
In total we have less than about 30 law enforcement agencies nation-wide - including state police, military, fisheries, federal police, prisons and border control.
It's my understanding in the US there are many many police agencies - per county as well as schools, banks, etc. Which adds up to around 18,000 over 50 states.
For our schools or shops we have security guards which have different training and far less powers than police. They basically have the similar powers to a normal citizen. They are used more as a deterrent rather than anything functional.