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.