A logo for a brand is what makes the identity, and the three cannot be put on a different platform since they connect in the larger framework of the digital medium. Although the three come under the same umbrella, they operate on different levels. Together however they form the ultimate face of the brand and company from a business point of view.
The corporate image of a brand is far more complicated than one may think. For a layman, the brand includes a bunch of colors, cool images and a whole lot of text, but in truth there is a greater science and thought process that goes into making a brand, let alone a solid one. The fundamental idea behind a brand is that it showcases all that the company does and also brings to light the vision of the company. If we take Apple for example, the brand is what the company's vision or outlook is towards the products that they sell. The core element of a company is what ultimately gets highlighted in a brand. The humanistic element of Apple is what clearly gets spelt through the brand image on a larger scale, and this is something that the consumer connects to.
Identity of a brand is the respect and image that a company garners from their target audience. Whether it is a big company like Coca Cola or whether it is a smaller scale IT firm, the identity is what matters when it comes to sustainability of consumers.
Last but not the least is the logo of a company. Simple, clear and to the point is what makes great company logos. If you look at Nike, Adidas, McDonalds, or even Ford, the logo is simple, crisp and is devoid of any high flown images or texts. A successful logo is the kind that catches one's attention in a heart beat and stays in the reader's minds for several days or months.