There are two popular definitions of a web designer.
First is a UI/UX designer. A UI/UX designer works with tools like Photoshop/GIMP and Figma. A designs how a website user interface should be.
Third is a frontend developer. In addition to the skills of the frontend designer, a frontend developer should be able to create reusable modules for the frontend. This can be done by using a framework like React or Angular. Also a frontend developer might have experience in using some libraries like jQuery, Lodash and Dojo. He must have a little bit knowledge about how the backend is designed so as to be able to work with backend developers.