When the term brand is used it is sometimes confused with the idea of logo & identity. Sometimes the terms even start to be used as if they were interchangeable. This is a mistake.

Confusion is quite understandable because brand means something both more broad & more specific than either logo or identity. To make this still muddier A brand is sometimes the identity of a company - or it can refer to a single or a group of products & services apart from the company.

Examples

IBM, Exxon, Sony & Nike are examples of brands where the company brand is more important than the the name of any specific product.

The opposite occurs as well. For instance Crest toothpaste is better known than its parent company Procter & Gamble. The brand Kleenex is better known than its owner Kimberly Clark. Mercedes Benz is better known than its owner Daimler Chrysler.

Sometimes there is a blurring of the line - does 'Levi's' refer to the product (jeans) or the company. The answer seems to be yes to both.

Consumer centric

One way to distinguish a brand from an identity is to remember that a brand is usually talked about only in the context of consumer products & services rather a business to business context.
In this way the term brand is more narrowly defined than either logo or identity.

Becoming a brand

Perhaps the best way to think about the term brand is to recognize that while a logo or identity exists as soon as it is made, it does not become a brand until it has become very successful & well recognized.

In this sense the term brand is broader than the term logo or identity because it can refer to a successful version of either thing.