DLG, digital line graph, is a form of a digital map created by the USGS that uses a topological vector model. This is a DLG map of Columbus, Ohio. http://daniellemapcatalog.blogspot.com/2008_11_01_archive.html
A propaganda map is very similar to propaganda cartoon. It portrays something in an inaccurate way or created using subjectivity with the goal of persuasion. They cartographer draws the map for the same reason a cartoonist would draw a propaganda cartoon. In the map you can see how each country was seen through the eyes of a Dutch cartographer. It shows how each country acted toward each other during that time period. http://dish.andrewsullivan.com/2013/07/22/maps-as-political-tools/
PLSS, Public Land Survey System, is a way the United States divides the land up. It is normally used for rural areas or undeveloped land. The map that you see here shows how Florida is broken up. It separates the counties to show how much land each county uses. This is a PLSS map because it shows how the land is split up between the counties. Granted it isn't a rural area but it does portray the land use.
http://cartographic-catalog.blogspot.com/2012/04/public-land-survey-system-plss.html
A cadastral map shows the property area of a city or region. It shows the space of each land. For instance a cadastral map of a neighborhood would show the size of the land that each house can occupy. In the map here it shows the historical map of Washington D.C. and how much each building occupied.
http://www.dcvote.org/trellis/character/historicalmaps.cfm?print=1
Thematic maps are used to portray an area and apply a theme to it. The theme can be social, political, agricultural, and other aspects to define a city, region or country. In this map it shows what political party is running each state in 2007. It portrays how the Republican party was running the majority of the United States. This map shows how a thematic map works.
http://www.gigawiz.com/thematic.html
A topographic map shows the natural layout of the area. This map shows the topographic layout of all of Australia. It shows where the desert, mountain ranges and the basin. This map is a prime example of what a topographic map is.
http://www.nationsonline.org/oneworld/map/australia-topographic-map.htm
For this map it conveys a planimetric map. A planimetric map is when a map shows a grid-like structure on the map. It shows the layout of the area without showing the elevation of the area. The map that is portrayed here shows the layout of city of Manhattan and all the streets and neighborhoods within the city.
http://similaritymatrix.blogspot.com/2009/09/planimetric-map.html
This map conveys what the typical college student sees the world as. It classifies as a mental map because it portrays what the student sees in their mind but in reality it truly isn't what the world looks like. The map shows the world as smaller version of an actual map. In this map, the land masses are significantly smaller than the Atlantic Ocean. The Pacific Ocean is a lot smaller as well. This is a great map to portray a mental map. http://lacamina.blogspot.com/2008/09/mental-map.html