The problem is definitely with naming. Regardless of whether you have

    function neigh() { ... }

or

    class horse {
        method neigh() { ... }

You still wind up with "add functionality for this _slightly different case_" and the code gets modified in exactly the same way. It's not until you clear up that you're dealing with different things, with different names, that you can start to make the code clearer. Because you need to be able to talk about the things in the code.