[mbivert]

I believe that a good definition of the "core" functional programming is: it's a practical way of using the λ-calculus. Similarly, imperative programming is a practical way of using Turing machines.

It's always somewhat possible to express what are typically considered imperative features in a functional fashion (e.g. monad), or bend imperative languages to behave somewhat like functional ones: I think the differences become clearer once we reach out for the underlying theoretical models.