I would call a language like Haskell "purely functional" and a language like OCaml "impurely functional". A functional programming language to me is a programming language where functions are in charge of data. In a language like Java, data is in charge of functions (broadly speaking). In a language like Prolog, relations are in charge of data. It's all about what perspective the programmer has between the abstraction and the data.

You have it backwards. In Java, collections of procedures (aka objects) are in charge of data. In Haskell and OCaml, data exists independently of the procedures that will operate on it.