I just went to the web site for the first one (ArcGIS Web Application). Luckily the road name was on screen shot.
It’s not a private road. It’s an extension of the right of way that hasn’t been paved yet. If either of the adjacent property owners tell you that you’re on their property (and you’re in line with the paved section behind you) they are wrong. They may be lying, attempting to take public property. What you do about that depends on many factors, including whether they’ve got a gun or a mean dog. You COULD to choose to call either the city or county, depending on whether you’re in the city or the unincorporated county.
I’ve run down several dirt roads and tracks in Deland. They make a nice break from running down cement sidewalks.