[greydius]

From a mathematics perspective, they're a property of mappings between two categories (called functors). I think part of the confusion us simple programmers have (aside from no knowledge of category theory) is that these words are used without explicitly stating what categories we're dealing with. In the case of typed functional programming (e.g. Haskell), we're usually thinking about functors as mappings from the category of types, where the morphisms are function types, back to itself. But in the object-oriented world, these words are usually used in the context of a category of types where the morphisms indicate a subtype relationship.