What is a "web designer"?
The field of website creation is a vast one, with many different skills needed to complete a single site, ranging from creative design, to imperative programming, to natural language content creation. With so many different skills needed, it is often hard to figure out what one should learn when trying to apply themselves to a certain role, for example that of a web designer.
Web designing is perhaps the broadest term that can be applied to such a person. It may cover both the creative design and technical sides, and indeed the entire process, of creating a website, from start to finish. But what does one actually need to know? It is necessary to be able to write HTML, or even code JavaScript, or does one only need to be a graphic designer? And in my opinion the answer is, well, it varies.
I do know of a few designers who are completely hopeless at any form of coding, and rely on developers or PSD to HTML services to convert their designs into reality. Of course, it helps a lot (if you are a web designer) to know the fundamentals of front-end development, but it really depends on the role you are taking – for example working as a designer in a large agency who may do web work versus working as a freelancer. Also, I really wouldn’t expect a web designer to know JavaScript beyond the very basics. That is very much in the realm of front-end development. But the more skills the better – if you are both a Cinema 4D geek and a JavaScript “ninja”, then good work! But it is very hard to focus on everything, and if you can produce brilliant designs but don’t know the difference between divisions and spans, I wouldn’t hold it against you.
In the end, every organisation has their own requirements, and each one may define the position “web designer” differently. There is no “one true” skill-set that such a person needs to know – one can focus on having a wide range of competencies, or focus on perfecting one skill, and each will open up different opportunities. So just study what you wish, and there is sure to be a place for you, somewhere.