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Many world maps, especially old ones, often have shaded country outlines in a particular color. The saturation becomes weaker towards the inside of the country and is strongest at its borders. Here is an example of what I mean:

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Is there a correct term for such a map style?

This style does not just appear in historical maps, but for example also in this National Geographic map of Europe from 1962.

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    I think it's called an antique style political map. – farrenthorpe Feb 22 '18 at 6:25
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    You should follow the Geography Stack Exchange proposal and post this as an example question there -- it's a perfect candidate for a geography SE, and the proposal could use a bit more support. – Pont Feb 22 '18 at 8:50
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In cartography they are called "tint bands", or sometimes, a "verge".

In GIS software it's a "shapeburst fill" (QGIS) or "buffered gradient fill" (ArcGIS)

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