A continuos development model is far more effective for web development than a standard cycle. Why? There are plenty of reasons, the biggest difference is that a website is mainly a marketing tool while conventional software is based on functionality. As you might have experienced websites are never finished. Great websites evolve constantly to keep up with the market. Web surfer expectations increase every year. They desire better functionality, up to date content and cool designs.
The concept is simple, the customer purchases a fixed amount of hours of development per month. These hours are used to enhance your website in every aspect.
I'm going to make a generalization on this topic and may not be correct on a case by case basis. Most of these titles are a figment of marketing anyway. However both developer and designer profiles exist and are usually easy to spot.
Web designers are usually artists or graphic designers who end up building websites. Their sites are flashy and creative. The downside is that they usually lack the rigor of analysis, in other words they lack engineering.
A web developer in contrast will treat your website as software and as such will follow due analysis and process. He will not sacrifice functionality, navegability or SEO over presentation.
In my case being a software engineer by trade I rely on a symbiosis with artists to build a website. I consider design a mision critical function in the software development cycle.