I think the first one is a single function that has pattern matching for the parameter while the second one is defining the function twice and relying on the language to call the right one based on the parameter.
I think in Erlang the function identification is the name and the arity and this is as close I know of what you would like to have.
Semicolons separate partial definitions for a single function of a single arity, and periods end those definitions. Removing the punctuation might make parsing a bit more difficult (will there be more partial definitions?), so it's understandable to not offer it.
I'd imagine you could compile them both down to the same thing, as there has to be a conditional at some point to determine what code to run (unless there was some kind of dynamic dispatch), I think it's just a matter of preference
I think in Erlang the function identification is the name and the arity and this is as close I know of what you would like to have.