In general, Sheriff is just a different name for small town police. They'll have the same powers, legal strictures, etc. Traditionally, sheriffs are associated with more rural areas, while police departments are in more metropolitan areas. This can depend a lot on area: Los Angeles, for instance, has police for the actual city limits and sheriffs for the greater LA county. But because LA is so built up, the Sheriff's department there is organized pretty much the same as any other police department, with a detective branch, differing ranks, etc.
I assume you're using a somewhat small town setting here, so there'd probably just be a sheriff and a few deputies (actual ranks and titles would vary be town, but that's the most generic). The main differences are going to be resources, and job descriptions. In a small town with a lower crime rate, there's going to be less focus on solving crimes and more on general peace keeping- solving domestic disputes, breaking up fights, that sort of thing. If a major crime (such as murder) were committed, the department may need to call in some sort of expert, most likely from the state police. Smaller departments aren't going to have much in the way of forensics labs or the like, and may have to send evidence out to be handled. One advantage that they would have is knowing the people and the area, since there's much less to watch and they've probably grown up in the town.
So, basically, you can probably just have a sheriff and a few deputies in the town and not worry about the difference too much, unless your players are really concerned with legal structures and the like.
I'm not a lawyer or any kind of expert, someone with actual experience may be able to add more.
I don't think any of my players are going to get too bogged down in the details, but I did need to check a few things.
