Website builders are tools that typically allow the construction of websites without manual code editing. They fall into two categories: online proprietary tools provided by web hosting companies. These are typically intended for users to build their private site. -Wikipedia
For most people looking to get a website going, they will either find themselves at a GoDaddy or Wix from all the ads you find on the internet, radio, or TV. Lots of people from your everyday neighbor, to famous celebrities, telling you how easy and quick it is to get up and going, and they are right.
These tools are used to get a basic website up and going quick. You can sign up for a service with one of these companies, drag and drop content on top of pre-made themes and your good to go. The ease of these tools makes it so just about anyone can get up and go in minutes.
A web developer is a programmer who specializes in, or is specifically engaged in, the development of World Wide Web applications, or distributed network applications that are run over HTTP from a web server to a web browser. -Wikipedia
A Web Developer in a more general description is someone who will take just about any idea you have for your online presence and make it a reality. If you know you want buttons in the center of the screen with text only over one of them and each letter a different color, font, size, AND then you want the letter to jumble up everytime the mouse hovers over and creates a new random word with new colors, fonts, and sizes, and then… and then…
This is all possible with a developer. You tell them what you want and like magic (not really) you have it on a screen. A developer removes you from the preset themes, and drag and drop the boxes, and gives you customization.
A web designer is someone who is both creative and technically inclined, and uses both these attributes to build or redesign websites. The web designer has the ability to understand what is needed to make a website functional and easy to use, but at the same time make it aesthetically appealing to the user.
This is a more common search then web developer, a designer has most of the capabilities of a developer, but with the added bonus of creativity. Designers have the eye for UX (User Experience) on your website/app.
If you come to a designer with some drawings and say this is what I want, most designers will give you some great feedback to what you should keep and what you should add. They will allow for the full customization and add to it, making it easier for your audience to navigate and want to stay on your site. They will use colors, fonts, animations, anything to attract the eye and keep your users engaged.