Oh my bad. I’m from the UK and not up with the lingo in the US. Sorry for any confusion
No worries. Its like this: The sheriff's department covers the county which is the larger area containing all the towns, any cities and rural areas. The Police Department is a city entity and they are responsible for everything within the city limits but not beyond. The county sheriff is sometimes called upon by city jurisdictions within the county to reinforce. I hope this makes sense.