When you change the look of your WordPress website, we're normally talking about changing your theme. A theme controls the layout, colours, and fonts of a site.
It is a preset package which contains a lot of information about the appearance and function of a website -- it's like a framework, or skeleton, that shapes the content you put on your site.
Commercial themes are designed to appeal to as many people as possible, so they often have a lot of features that your particular site doesn't require. They may also not contain features you regard as essential, which means that you need to customise the theme or use plugins for those elements.
A full site redesign, or redevelopment, means the developer is creating a custom theme just for you. This is definitely the best option from a user experience, as you get a site that is designed especially for you and your site users -- it's created from the ground up, and all the functionality is exactly what you need. There's no extra weight to slow things down.
Full redevelopments are priced to reflect the work that goes into them, so they certainly aren't the cheapest option!
Performance Foundry specializes in creating beautiful, high-performance sites: have a look at our seven-step process to get an idea of how we work with you to create a site that is tailored to your visitors' needs.