Trains and Maps
There are a few basic models for classic transit maps. Some of the biggest transit systems also exercise considerable design influence on other systems. One basic model is New York's transit map. However, New York is redesigning its map. Here you can see the New York map over time. As can be seen, New York is maintaining the general style of its map. While the lines are not perfectly coordinated with the city above, effort is clearly made to integrate the subway with the street grid. The redesign simply updates some information, and zooms the densest area while de-emphasizing some less congested (though larger) areas.
In contrast, London's transit map is made without any reference to the street grid above. Instead, it is straight lines, and 45 degree angles. London is probably the gold standard for transit maps. In many ways Berlin (and 0ther major German cities) are modeled on London.
Montreal is one of a few cities that has a map that is base black and printed thereon. For the most part, it seems to be something Gallic, as the others with this color scheme are usually Francophones.
Interestingly, the current Chicago map is largely representational (like London), but includes angles that are not 45 degree angles. However, the CTA also issues a map that is much more closely tied to the street grid. To this extent it is more like New York. The general system displayed on the trains and in the stations is the representational version, but the street grid version is the star of the map handout available for home study.
Anyway, there it is.