Mapping

In mathematics and related technical fields, a mapping or map is a variation on the theme of a function.
Most commonly, the terms are simply synonyms for function. Along these lines, a partial mapping is a partial function, and a total mapping is a total function.
In many specific branches of mathematics, the term is used for a function with a standard property relevant to that branch, such as a continuous function in topology, a linear transformation in linear algebra, etc. In Wikipedia, we always include a relevant adjective like "continuous" or "smooth" to avoid confusion.
In formal logic, the term "mapping" is sometimes used for a functional predicate, whereas a function is a model of such a predicate in set theory.
In computer science, a mapping is the relationship between a key and its value in an associative array.
In cognitive psychology, a mapping is the relationship between a source domain and target domain, typically reflecting a conceptual metaphor.