An API (as people usually mean by it, anyway…) is really just a simple grammar for the creation and manipulation of objects in the system. Those objects still have types and properties just like any other object, but they tend to be implicit and unreliable. A good DSL is just a more abstract and implicitly verb-oriented API. For example, Lua DSLs can resemble something almost like a sort of typed or tagged DDL. Translating that into an “API” just adds more clumsy legwork to achieve the same outcome.