What makes some API's become DSL's?

What causes an API to cross the line into becoming a DSL? Is it really a 'I'll know it when I see it' situation? I've been searching for an answer for years. And I think I found it in a paper I read recently for this podcast: Lisp: A language for stratified design. In this episode, we go over the main factor that makes an API a DSL: the closure property.