A company’s brand identity or a brand's brand identity (if a company own more than one brand) is the way in which it is defined through its style both visually and the values it portrays (its brand personality).
There are 3 types of brand identity:
The whole company presents itself as one both visually and in the way it communicates and behaves. BP and Burger King are good examples of that type of corporate brand identity.
Subsidiary brands have their own style and identity but pay homage to their parent brand which is clearly presented in the background. Subsidiary brands can have their own personality but are still endorsed by their parent brand. A good example of this is car manufacturers who have a series of sub-brands but are each new brand of car is still heavily associated with its parent brand.
Each division has its own identity and style but product lines do not have anything to do with each other or the parent. This can be as a result of mergers and acquisitions where existing brands with strong identities do not want to be merged with their new owner.