A lot of times you can add clarity to a subject by adding terminology.
This is such a case.
“Brand” is what your product, service, or company means or stands for, hopefully in the minds of your market.
“Brand Identity” is everything that symbolizes that brand.
A logo is an example of brand identity. It doesn’t establish your brand – though it can help. If skillfully done, it can come to symbolize that brand. When Starbucks was first starting out, their mermaid emblem didn’t mean a thing to anyone except perhaps the owners of the company and the designer.
Now, hundreds of millions of people can see that logo and know immediately that this is a place where they can get a good, if pricey, cup of coffee.
Color scheme, tagline and other brand identity elements work similarly.
Nike’s ads breathed life into “Just Do It!” – not the other way around – and made their famous “swish” logo stand for the same thing. That the logo fits the sentiment and the ads dramatized it, is a matter of integration and consistency – both essential if branding is going to work.