The whole Sheriff/ Cop thing question?

Most U.S. States have counties and each county has an elected Sheriff for that county. Within the county may be several incorporated cities all of which may have individual police departments headed up by a chief of police.

The Sheriff or his/her deputies have jurisdiction over the whole county including the cities. The Sheriff, in most cases is considered the top law enforcement official of the county.

The sheriff is an elected position and therefore very political. The chief of police is mostly and appointed position.

This movie, or at least the portrayal of how they treat the high Sheriff is pretty unrealistic

This is just a quick rundown

Sometimes when you want the devil, you have to go to hell and get him!

Typically a Sheriff has jurisdiction over a county (although only the city is mentioned in the movie). Sometimes the incorporated cities within the county allow Sheriffs (and their deputies) jurisdiction within those cities inside the county as well. A sheriff also has other less 'cop-like' functions: providing basic court related services such as keeping the county jail, transporting prisoners, providing courthouse security and other duties with regard to service of process and summonses that are issued by county and state courts. The sheriff also often conducts auction sales of real property in foreclosure. So these other 'lesser' duties may give the impression that they are not 'real' cops. Often they are paid less than the city police. Other less common law enforcement titles are constable and marshal which may or may not have similar or more police like functions depending on the locality. Job titles vary somewhat so you would have to know the details to be sure what the difference is and who is considered more of a cop.

I don't think being a sheriff isn't seen as being inferior to being a big city cop, it's because he's Sheriff of a such a small town where not much happens and he only has 2 deputies, whereas naturally the NYPD cops work in a tougher environment. But many Sheriffs probably command a lot more than 2 deputies and have greater responsibilty, prestige and pay than any of the cops in this film.

The cops lived in Garrison NJ but were working for NY city. They had no jurisdiction as law enforcement in Garrison.

Police are city law enforcement and the Sheriff and Sheriff's deputies work for the county and yes there is some over lap. In the film these were NYC cops who were just living in Garrison.