Brand and identity are pretty easy to conflate, as they both answer the question, “who are you?” To understand the difference, we can take the metaphor a little further.
Identity is your social security number. It’s the token to play. if you were strictly speaking in identity terms, when asked ‘who are you?’ you’d reply with your name.
But, to answer ‘who are you’ with your credentials is a shallow dip into the pool. This is where brand comes in: what makes you inherently you? It’s the swagger and the voice that make up a brand and ultimately speak to your essence.
There are plenty of companies that do both, one or neither of brand and identity well (some more intentionally than others).
Examples of companies with strong identities and strong brands:
Nike, Levi’s, Penguin books, New York Times, Virgin America, Coca cola, Nintendo, Apple, PBS, Gatorade

Examples of companies with strong brands and weak identities:
Urban outfitters, Wikipedia, Many fashion design companies, Ray and Charles Eames, The Smithsonian
Examples of companies with strong identities and weak brands:
CBS, FedEx, most car brands, public transit systems

Companies with strong identities are immediately recognizable, and companies with strong brands are easy to relate to. When a company has a strong identity and a weak brand, it seems like a utility. It’s easy to find when you need it and different from its competitors, but you don’t expect it to have much personality.
Companies with weak identities and strong brands feel extremely democratic and mercurial. They can be rooted strongly in trend or the flow of the people. For Urban Outfitters, for instance, a lack of identity actually strengthens their brand. They appeal to irreverent, young renegades, and their damn-the-man attitude is amplified by their ever-changing logo.

The reason a strong identity and strong brand is the holy grail of companies is because only when utility and ethos are combined can a place really portray itself as a service. However, it is an interesting thought experiment: what would happen to your company if you leaned one way or another? Is one side more appropriate?
All good things come to an end. Or, they would if we ever stopped evolving.
There are two kinds of reinvention. A company that’s settled into a comfortable and wan pattern will shake up its brand to fly under a steadier standard. Take the Current TV redesign, which does this quite literally:

(image from Brand New)
The idea of an army-sized movement, of the immutable power of the tide, of a billowing flag in the dark—that’s got a lot more heft than techy crowds wielding pixels. And, it’s what Current has always been about.
There’s a different genius in the second kind of reinvention, the reinvention of conviction.
Sunglasses are built to shield us. They block out the sun, they anonymize movie stars to the flash of the paparazzi. I have always loved Ray-ban for its complete opposition of this idea. Let the other sunglasses keep out the world. Never Hide in Ray-bans.

Jeans are built for hard, gritty work. But, in Levi’s, there’s work to be undone. In the nostalgia for our forefathers, we don’t find factory drudgery. We find the love of careful craft and the freedom of razing the past to start anew.

When your brand’s heart runs dry, find a new north. Run in the opposite direction. Free yourself from the metropolis we’ve built and head for the frontier. Breathe the country air. At the very least you will come home changed.

Let’s shoo the clients, bosses and managers out of the room for a second and talk about process.
Process is the bugle call of our design generation. It propagated with the IDEOs, frogs, Zurbs and Smarts of our industry and infiltrated every company. Finally, the heady coven of creation, distilled into phases and checkpoints—this was something the most empirical CEO’s could understand and salespeople could sell.
That’s wonderful. My parents don’t call me every night worrying I’m dumpster diving, and human beings have access to better designed objects as a whole.
Backstage, though, I pray to the design gods that we ourselves aren’t drinking this simplistic koolaid. Problem-solving and brainstorms are vital, but simply following the process we outline for non-designers would yield (and has yielded) unremarkable work.
Ouch! But, really, the ‘design process’ is bland, mechanical and easy. A problem comes in. You arrive at solutions, pick the winner and push that baby out into the world. It isn’t the interesting part of design at all. What really makes a brilliant designer is the white space between the outlined gospel. What creates the visual metaphors, the right questions to ask or the right shade of pink? That designer’s particular experience, whether it be school, work or play. There are hidden wells inside of us that don’t surface in explicit ways.
For example:
Even if you’ve known me for years, you might not know I watched nature documentaries every day for five or six years. Mental space for reminders and algorithms is filled up instead by seemingly useless animal facts. Besides helping me remember the names of conference rooms at Twitter, this experience gave me respect for systems and symbiosis, a sense of scale, and an eye for movement and detail, among other things. I didn’t know it then, but this antisocial TV habit was inherent to my personal design development, and vital to my career.
We create in the context of ourselves, and that’s not something easily quantified. I could never tell a client, here’s a charge for the hour I spent watching that Discovery documentary about salmon migration fifteen years ago. I couldn’t have found this solution without it. There’s no proof and no deliverables for that time. To the rest of the world, that’s nerve-wracking, but to us, it should be comfort that the best method of interesting work is to seek out experiences and learn how to let them change you.
Sell, and sell well. But never forget—each day is part of your process, and that you’re preparing for a project that may be years in your future.