Map
A map is another word for mapping. These two terms are short for "linear map" and "linear mapping", respectively; both of the terms come from linear algebra, where they are also synonymous.
In the writings of Dave Keenan and Douglas Blumeyer, their convention is for "map" to refer to a single-row map/mapping, and "mapping" to refer to a multi-row map/mapping.
A val is a special type of map.