They don’t, but they can :)
Branding (it’s more than a logo) means getting to the heart of who you are, what you do, and why. Designing branding along with your site creates a cohesive, authentic online presence. Many of my clients already have branding, so I leave it as an optional addition for projects that require it.
For businesses who don’t need a complete rebrand, but could use some sprucing up, we often do a refresh. That usually includes adjusting the color palette, changing the company typefaces, sometimes rotating some of the logo elements to perform better through varied media. (You can see an example here. )