Earlier quoted context omitted.
It seems you need more time to think about it. Message passing can be synchronous, and function calls asynchronous Also consider remote procedure calls.
A function is well defined in mathematics; see http://en.wikipedia.org/wiki/Function_(mathematics) . Note that the definition doesn't really differ for computer science. Procedures, on the other hand, may or may not be functions according to whether they behave like them (match their properties).
This latest response seems to be entirely based on hooking into the word "procedure" which occurs in "remote procedure call". I don't do Eliza, sorry.