The "US17Con" labels probably derive from South Carolina's GIS reference, which defines that route as US 17 Connection.
I would be in favor of what Mapmikey suggested above. Is the "connector" a ramp? Maybe, but it is definitely intended as the mainline for southbound traffic on 17 Business, and it even has a couple separate intersections south of where the route to Murrells Inlet jumps off. That southbound signage could also be interpreted as a new business route beginning to the south, with the mainline 17 shield simply intended to avoid the confusion that results from two Business 17s intersecting.