Is Erlang really a functional language?

The central idea is that each process is a functional program over an input stream of messages. The result from the functional program is an output stream of messages to others. From this perspective, Erlang is a rather clean functional language; there are no destructive updates to data structures (like setcar in Lisp and most Schemes).

With few exceptions, all built-in functions such as operations on ETS tables also follow this model: apart from efficiency issues, those BIFs could actually have been implemented with pure Erlang processes and message passing.

So yes, the Erlang language is functional, but a collection of interacting Erlang processes is a different thing. Each process is an ongoing computation, and as such it has a current state, which can change in relation to the other processes. Even a database is just another process in this respect.

In my mind, this is one of the most important things about Erlang: outside the process, there could be a storm raging, but inside, things are calm, letting you focus on what that process should do - and only that.

Yes, it's a functional language. It's not a pure functional language like Haskell, but then again, neither is LISP (and nobody really argues that LISP isn't functional).

The message-passing/process handling of Erlang is an implementation of the Actor model. You could argue that Erlang is an Actor language, with a functional language used for the individual Actors.

The functional part is that you tend to pass around functions. Most langauges can be used both as a functional language, and as an imperative language, even C (it's quite possible to make a program consisting of only function pointers and constants).

I guess the distinguishing factor is usually the lack of mutable variables in functional languages.