Not so sure about that. JavaScript is a quite advanced language, below the surface. To be able to do anything non-trivial in JavaScript, you have to be a developer and have to have a good understanding of Computer Science.
Also, I don't do any "design", in the creative sense. I implement the design of my partner. So I think your terminology is wrong.
JavaScript for AJAX and loading new information would be developer yes, because that is all about querying and interfacing with the back-end.
Simple visual JavaScript effects for enhancing presentation and interface would be web-designer.
To me the key part of the term "web-designer" is web... you are creating design using the assembly languages of web browsers: HTML, CSS, JavaScript, and small quick-to-load chunks of graphics. Drawing is just the first planning step and there is nothing that makes it "web" specific other than an intention. Whereas in "graphic" design this is the end result. A graphic designer designs instructions for a graphics display process to display graphics, a web designer designs instructions for a web browser to display web pages.
Also, I don't do any "design", in the creative sense. I implement the design of my partner. So I think your terminology is wrong.