The web designer deals mainly with the visual or aesthetic aspect of a website. He is in charge of colors, fonts, images, layouts, etc. Their main goal is to visually enhance your website.
Web programmers help you create your website. They work with the coding aspect of a website. Their main concern is the construction and functionality of the website.
When choosing a web designer or programmer, be sure to check their online portfolio to see if they have done projects in the same scope as yours.
Don’t trust those who only show a picture of their work without giving you a chance to test the website live. Don’t hesitate to ask for references.