Logos and Favicons are both visual elements that help create brand identity.  The logo is the primary visual representation of the brand.  A favicon, short for “favorite icon” is smaller more functional visual element.  Favicons are usually found on the browser tabs, bookmarks, and browser history.  Typically a favicon is just a simplified version of the logo.  

The main difference between the two is their purpose. A logo is meant to build and communicate a brands identity, while a favicon is designed to help users quickly identify a website.