I find the term "web design" to be contestable.
I have a friend from college who is a "web designer" , for a large development firm but the doesnt even know CSS or even HTML.. not even tables!! What he does is he build graphical elements in ADOBE photo shop/illustrator/ indesign for wed pages. So since he does "graphic design for the web" he doesn't consider it a misnomer to for his title to be "web designer"
Other folks may not be very good at using photoshop, or MORE IMPORTANTLY , have no aesthetic sensibilities whatsoever but are MASTERS at HTML and CSS. They can solve cross browser issues and write CLEAN , SEMANTICALLY MEANINGFUL markup. Despite remedial "artistic talent" these individual also claim the title "web designer"
PERSONALLY, I break it down this way:
GRAPHIC DESIGN: pretty pictures, no code
WEB GRAPHIC DESIGN: pretty pictures, fit to wrap around code
WEB DESIGNER : Code(HTML) , layout (CSS), semantics, cross browser checking, web graphic design skills a +
WEB DEV: PHP, .NET, .ASP, FRONT END SKILSL a + , SQL/MySQL a + , knowledge of servers +
BACK END admin/DEV: SQL/MySQL ( and other types of DBs ), PHP, .NET, .ASP, knowledge of servers .. front end dev skills kinda irrelevant, but why not mention it if you have them.