'Tour' doesn't have to be in a vehicle. You can go on a tour on foot, too. Many cities organise walking tours with guides. And yes, if you visit a castle, for example, you can choose to visit it on your own or go on a guided tour around it.
'Sightseeing' means looking at the well-known sights in a particular place. 'Going on a tour' or 'taking a tour' means being shown around a place by a tourist guide, usually with a set itinerary.