Graphic design is the entire subject, web design and postage stamp design are two aspects of it.
Coding, etc., are web development, not web design.
You have to be a graphic artist first, then you can specialize in one or more aspects. Web design, though, isn't that creative, it's more "art for hire". You're told what the design criteria are and you come up with the design. It's art in advertising, applied to a single medium.