indeed. A permissive path is one over which a person has permission to travel but no right to do so. A private road could be a permissive path. There may be restrictions on what a person may take with them.
A public highway is a route over which there is a right to travel. There may be restrictions on what you can take with you. A public footpath is a highway on which it is not permitted to take motor vehicles, horses, or cycles (except in Scotland where the rules are a bit different). A motorway is not a public highway as there is no general right of way, but way is only permitted for those in vehicles of a certain class.