What branding means
The American Marketing Association defines a brand as any distinctive feature, such as a name, term, design or symbol, that identifies goods or services. Branding is what you do with that feature: decide what the brand should stand for, how it presents itself and how it stays consistent at every touchpoint, from the website to an invoice.
Three things are often mixed up. The logo is one building block of the visual identity, and so only part of the brand. The brand is the idea the public connects with a name. Reputation is what the public thinks of that brand, based on its own experience and on what others say. Branding works on the first two and influences the third only indirectly.
In digital marketing, branding also has a technical side. Search engines and AI assistants do not see a brand the way a person does: they piece it together from names, links, structured data and mentions spread across the web. If those pieces do not fit together, the brand breaks into several.