Ok so it might be really simple sure - but the point is that people mess this up all the time. Why & how?
A business model is how you make money. For example you sell time, you sell products, you sell something else... think of it as where the money is made and where the money goes. That's the business model. It's the excel part of the business... what are the critical variables, what are the fixed costs, where can it go wrong, where can it go so right? This is not to say that everyone has the same business model but I think you get what it's about now.
So what's the brand - well the brand is more about the why, the promise to the market, how you communicate to the market etc etc etc.
So where do people go wrong? All too often people don't separate these two things in their head, especially when they have a few brands going but really they are just playing around trying to figure out how to best make money with their one business model. I mean playing around is probably a bit much in terms of language. It's kind of just a brain process as people try and figure out what to do and how to do it.