A brand is defined as the perceived emotional corporate image of your business as a whole. What your brand is, is exactly what it makes people feel.
A brand identity is basically any visual aspect that forms an image of the overall brand. The brand identity you craft will control how you want potential consumers to perceive you.
A brand alone doesn’t represent what your company is. Neither does an identity or a logo. A logo is not your brand, nor is it your identity. All three of these are independent standalone aspects that must come together strategically to form the image of your brand, or your business.