symbol map: symbols represent phenomena; symbols may just overlap or symbols may reflect overlapping by the way they are constructed with each constructing element (or the absence of it) being assigned to one of the mapped phenomena.
Think of shape, filling, grain, size, orientation, markedness. By focussing on one element one 'highlights' the appropriate phenomenon. The clarity of the map may be better served this way than having symbols stacked upon each other.
A symbol may just represent a qualitative phenomenon but it may also represent a class of frequencies or other type of measurements.
line maps: having established a symbol map first one may next draw a line between two places showing each a different symbol. Same symbols may group in single areas. Lines may cross when different phenomena are mapped together.
choropleth maps: quite the same as line maps the difference being the coloring of areas. Coloring allows some gradient to be expressed by, for example, shading. Line maps can also express gradience, for example by the use of different types of lines.
Meaninglessness of borders of colored areas is even greater when pre-fixed areas are used which are based on other (types of) knowledge. E.g. zip code areas or census districts.
When formulas are used to calculate the shapes of areas on the basis of the mapped data these area borders become meaningful. For convenience sake we refer to the (English) article on the reasoning behind the → Wattel-application.
A special category of maps consists of maps made by drawing arrows reaching from one place to another place. E.g. people may indicate which places they think of as speaking related dialects; by their number and the number of targeted locations arrows may seem to shape areas (or, reversely stated, blank areas may indicate borders).
It is recommended to keep maps clear and effective - one should therefore limit the number and types of data expressed on the map.
Once again, computers may be quite helpful in manipulating maps.