That's a good categorization, but it's not a definition. For example, the distance between Haskell and Clojure when it comes to allowing (or discouraging) mutation, is bigger than the distance between Clojure and Java. Which, BTW, I think is true. Imperative "FP" languages have more in common with other impure languages that are not commonly categorized as FP, than with PFP. Clojure, Erlang and even ML really are closer to Java than they are to Haskell. I'd argue that the line is between using the continuation abstraction (or the thread abstraction) vs. monadic composition to achieve side-effects (and it is ironic that more people -- probably orders of magnitude more -- use monads in Java than in Haskell :)).
Favoring immutability is a great property, but it is not a hard dividing line. The Java community started encouraging immutability no later than 2001, and Scheme was called functional long before anyone categorized its main features as "restricting mutation".
Favoring immutability is a great property, but it is not a hard dividing line. The Java community started encouraging immutability no later than 2001, and Scheme was called functional long before anyone categorized its main features as "restricting mutation".