People who need a website usually look for for web designers when what they often need is a web developer, and maybe a web designer too. The difference between developers and designers has been around ever since Tim gave us HTML back in '93. And the difference is important and huge.
Some web freelancers, and even established companies, are designers. They came into website production through a graphic design route - they did a graphic design course which touched on web design and they discovered they could use various tools (like DreamWeaver back in the day) to produce living websites from their static designs.
Essentially, for small websites there's nothing wrong with this at all, and they'll no doubt look great, they are designers after all. But what happens when the customer wants a new animated widget and it stops the slider from working because there's a variable clash? Or different mouse-over/slider effects not built-in to whatever template they're using? That's when a web designer needs a web developer.
We are web developers. We came in to this from a computer programming background. Personally, I've been coding computers up since 1985, so when there's a website development issue it takes me 2 minutes to sort out (usually!). In the early days developers needed designers to produce beautiful website designs for them because developers are by nature not very creative, but these days with image driven websites, simple material design and things like the Bootstrap framework available there's really not so much need for pure web designers. Having said that..
Designers are creative, developers aren't. Developers will not only make a design work as a website, but also make it fast and efficient.. Designers wont. It's this fundamental difference between creative design and logical coding that means developers and designers need each other on larger projects.
A good web designer will know the nuances of navigation and the presentation of pages across devices and produce the appropriate graphics for the developer to work up into a website.