It's a reasonable assumption to make, as the Sheriff's Department is the primary patrol and investigative agency in every other county in SC. I made the same assumption years ago when I started monitoring and gathering radio data.
You can read up on the administrative differences. There is still a Horry County Sherrif's Office, and the Sheriff is still the top "law man" in the county, but the SD handles judicial security, civil process service, jail operations and tasks along those lines. The Horry County PD is the primary patrol, investigation and warrants service agency in the county and is led by a Chief of Police. Not unlike Municipal police departments like MB PD, NMB PD, Conway PD, etc.
Given the legal problems that many SC sheriffs have had over the last 5-10 years, and the fact that the Sheriff is an elected official that doesn't directly answer to County Councils and can only be removed for cause by the Governor of SC, one can argue that separating these law enforcement roles is a worthwhile arrangement with some definite advantages. But given the small size population-wise of many SC counties, it's not necessarily a practical arrangement for those counties.