There seems to be an unnecessary bit of academic hair-splitting going on as what to call these things. If a map is a graphic display of the terrain indicating the relation of one place to another, then maybe they are maps. On the other hand, they might be highly stylized and very distorted displays that give you straight-line indications of how to get from one place to another; that is, the bottom display (the number 1 Metro line in Naples) tells you that if you start at Piscinola (on the left), you will go through the indicated stations to get to the last station, Garibaldi, the main train station in downtown Naples. The graphic display makes no attempt to describe the surface terrain; that is, that first station, in physical reality, is at 300 meters above sea level way up beyond the airport; more realistically, view it as 12 on a clock face. The entire stretch through the remaining 17 stations will wiggle and wind around and run counter-clockwise all the way around the clock face, down through 9 and 6 and come back up to about 3 o'clock at Garibaldi and sea-level. Such "maps" have been called "schematic line drawings." They help you get from one place to another.
Icon for Rome on the Peutinger map
One of the best-known of these whatchamacallits is the image at the top of this page, a small reproduction of the famous Peuntinger map (alias the Tabula Peutingeriana, Peutinger's Tabula and the Peutinger Table). It is a medieval map made by a monk in the 1200's in Colmar (in the Alsace region in north-eastern France) and is a copy of an ancient Roman map, a cursus publicum, a display of the road network of the Roman empire. The map represents the empire’s network of roads and cities, with marked distances and landscape features such as mountains, rivers and sea as well as icons of buildings to provide guidance to travelers, showing stops along the way. It is a parchment scroll, 6.75 meters long by 34 cm high (approximately 22 feet by 13 inches), assembled from 11 separate sections. It was copied in the Middle Ages from an original Roman scroll (no longer in existence). It is called the "Peutinger" map after Konrad Peutinger, who came into possession of the document in 1508 after it was discovered a few years earlier in a library in Worms.
The map is now conserved in the Habsburg Imperial Court Library (Hofbibliothek) of the Austrian National Library in Vienna. It has been copied and published a number of times since the Middle Ages. In 1898 a twelfth sheet was reconstructed and added to show the presumed missing sections of England and Spain (it is the first section on the left, shown in white, in the top image, above). The original Roman scroll upon which the medieval copy is based probably dated to the 4th or 5th century and was itself based on a map prepared by Agrippa (64-12 BC) during the reign of the emperor Augustus. And that map was engraved into marble and set up in the Porticus Vipsania along the Via Flaminia. That structure has not survived, but it and the "World map" are mentioned by Pliny the Elder (23-79) in his Natural History. The map was apparently kept up to date, at least until the Western Roman Empire collapsed, since it includes the later Roman conquests of Britain, Dacia, and Mesopotamia, but some anachronisms remain, such as the presence of Herculaneum and Pompeii, both of which were destroyed (and not rebuilt) in 79 AD by the eruption of Vesuvius (though they might have been left in the map as noteworthy landmarks).
As it exists now, the map shows Spain on the far left (the reconstructed page) and India on the far right. As with the modern metro map, the terrain is extremely distorted; all of Europe and North Africa are squeezed onto a narrow left-right axis, which you might call, for the sake of convenience, west-east (except that once you start moving in from the left, directions are so skewed as to be meaningless). In other words, although Spain looks approximately right at the beginning, the British Isles then have been flattened down to conform to the totally left-right configuration of the map. Then, Italy (about halfway along the scroll has been angled up to run left to right, as well. What looks like a very long river running through the map at the bottom is actually the elongated Mediterranean Sea. The bits of land sticking up at the bottom of the larger image in this paragraph are North Africa. The detail is amazing: the map indicates 555 cites or towns and contains 3500 other place names. Icons such as towers and buildings are abundant to indicate what kind of town you, the traveller, might be passing or stopping at. The map indicates distances between towns, showing seas, rivers, forests, mountain ranges, and 200,000 kilometers of roads.
In the section shown (above, right), I was trying to find my house. Bad Agrippa! Bad! Sloppy map-making! Yet Naples is there (lower center). Herculaneum, Oplontis, Pompeii and other familiar names are also visible. The Sorrentine peninsula is on the far right. The unnamed island out there has to be Capri, but I'm not sure. (I don't think it's Hawaii.) Small, isolated Roman numerals along the roads are distance markers so you know you only have V or VI more whatevers to go (probably Roman miles). Puteoli (Pozzuoli) is indicated and there is Lake Averno. The bottom-most road coming in from the left at the bottom is the Appian Way. It bridges the Volturno river, which then angles up and over to the mountains, the Apennines, running the length of this section of the map. The large red letters A, N and I are part of the word Campania that you would see in a wider view. It was a helpful road map. If you want to get from Naples to Benevento, go through Atella to Capua, hang a right and you will be on the road to Benevento. That is still pretty good advice. The icons are tough. The one just to the left of Naples (Neapoli)—the golden half-head sticking up might be the Flavian amphitheater in nearby Pozzuoli or...or...the catacombs of Naples...? or...half of a golden head? Send me suggestions.
There is a very well-done and scrollable version of the entire Peutinger map on Wikipedia at this link. It's at the bottom of the page.
All images (except the Naples metro map!) are from that Wikipedia page.