"Pure" is an adjective applied to "functional" so I don't see the conflation as odd. A language like JavaScript has first class functions, so it's a little bit functional. But no more than that, because most expressions aren't (mathematical) functions. Haskell is purely functional because everything's a function. (I/O primitives like getChar excepted, etc., etc.)
Meanwhile, languages like Haskell don't cheat quite as much as you suggest. Monads are functions, and even in the IO Monad you're doing purely functional manipulation of IO primitives. Think of it as a purely functional funnel through which the dirty data of reality is poured.
Meanwhile, languages like Haskell don't cheat quite as much as you suggest. Monads are functions, and even in the IO Monad you're doing purely functional manipulation of IO primitives. Think of it as a purely functional funnel through which the dirty data of reality is poured.