Branding is a strategy intended to shape people’s perception of your business, while graphic design is the visual component of the brand development process. Branding involves visuals as well as:
messaging (the tagline, values, mission, personality),
positioning (your brand’s unique place in the market and how it is different from others,
personality (traits associated with your brand, making it relatable to your customers),
experience (customer service, packaging, shipping, etc.), and
culture (how your people live your business’ core values)
You can have design without branding, but it would be hard to have a branding strategy without graphic design.