Is there a difference between message-passing and method-invocation, or can they be considered equivalent? This is probably specific to the language; many languages don't support message-passing (though all the ones I can think of support methods) and the ones that do can have entirely different implementations. Also, there are big differences in method-invocation depending on the language (C vs. Java vs Lisp vs your favorite language). I believe this is language-agnostic. What can you do with a passed-method that you can't do with an invoked-method, and vice-versa (in your favorite language)?
as a first approximation, the answer is: none, as long as you "behave normally"
Even though many people think there is - technically, it is usually the same: a cached lookup of a piece of code to be executed for a particular named-operation (at least for the normal case). Calling the name of the operation a "message" or a "virtual-method" does not make a difference.
BUT: the Actor language is really different: in having active objects (every object has an implicit message-queue and a worker thread - at least conceptionally), parallel processing becones easier to handle (google also "communicating sequential processes" for more).
BUT: in Smalltalk, it is possible to wrap objects to make them actor-like, without actually changing the compiler, the syntax or even recompiling.
BUT: in Smalltalk, when you try to send a message which is not understoof by the receiver (i.e. "someObject foo:arg"), a message-object is created, containing the name and the arguments, and that message-object is passed as argument to the "doesNotUnderstand" message. Thus, an object can decide itself how to deal with unimplemented message-sends (aka calls of an unimplemented method). It can - of course - push them into a queue for a worker process to sequentialize them...
Of course, this is impossible with statically typed languages (unless you make very heavy use of reflection), but is actually a VERY useful feature. Proxy objects, code load on demand, remote procedure calls, learning and self-modifying code, adapting and self-optimizing programs, corba and dcom wrappers, worker queues are all built upon that scheme. It can be misused, and lead to runtime bugs - of course. So it it is a two-sided sword. Sharp and powerful, but dangerous in the hand of beginners...
EDIT: I am writing about language implementations here (as in Java vs. Smalltalk - not inter-process mechanisms.