The main differences between the two maps is that Ortelius actually showed the whole world on his map, while Ptolemy showed only parts of it, or rather, the so called Old World.
The map of Ortelius shows the whole world, and all of its continents. Even though the map is far from precise and some places like the Antarctica are represented much bigger comparatively with the other continents and their sizes, still it gives a nice basic picture of our planet.
The map of Ptolemy is showing only the Old World, so it has most of Europe, Asia (with its northern and eastern parts missing), and the northern part of Africa, so pretty much it is a map that represent what people thought of the world size before the big geographical discoveries.
