This is a rather ill defined area of job titles at the moment. Consider the following jobs:
- UX Designer
- Web designer
- UI Designer
None of these titles directly imply anything about development. At certain companies these titles mean "developer who also designs X". At others these are completely separate job functions and the designers may never need to touch code, or they may only code to create prototypes as opposed to final working products.
The scope of expected job capabilities can generally be inferred from the size of the company. When Microsoft says Web Designer, they mean designer; you will almost certainly mostly do design. They have distinct, large teams for all areas of projects. On the other hand, at a small start up, you can probably bet that their "web designer" does a great deal of coding work.
This is something you'll have to clarify by reading the description and asking. If the job description lists coding responsibilities, clearly code is involved. As for how much balance between design and code, you'll have to ask directly; they may even be flexible.
This is a very fuzzy area so you're just going to have to look at what each company is looking for in their web designer/developer.
Now, if the job is graphic designer you can really assume Photoshop and Illustrator are going to be a large part of what you do rather than anything code related. Slamming "graphic" and "web design" together (as the only option) is a pretty terrible choice frankly, but I'd say many companies looking for "web developers" also (hopefully) look in the "graphic/web designer" section as well. Again, horrible categorization, but employers are hopefully looking for skills not job titles.