First of all you need to decide your focus area in Web Design & Developement.
Few years back the trend was like, a web designer does layout designs in photoshop and use any html tool (Eg: Dreamweaver) to create HTML files or hand code them. That means a designer used to design and develop html web pages.
Now, the time has changed and there are 2 groups of people evolved: Designers & Web Developers:
Their focus is completely on the latest design trends, Usability, Accessability. Wireframing, User research, etc. They just design layouts and User Interface elements in Photoshop and pass on the design files to web developers.
These guys are more focussed on creating XHTML, CSS , AJAX versions of the designs done in Photoshop. You need to develop your scripting skills to do this job well.
So, depends on your interest, you can be a Designer or Web developer or both.
Let me know if I have not answered you what you expected.