So what's the difference between a customer and a user? The former brings the food to the table while the latter just benefits from your service. Consider Google for example. It is highly likely you are at least their user. If you use AdWords, you are actually their customer. As a user you are a part of their product that they provide to the people and businesses interested in reaching you.
This duality provides a nice way to think about your business model. It isn't enough to get a million users if you cannot get any revenue. You will need some actual customers too to make it all work out monetarily. In order to make your business profitable you will need to figure out how to convert users into paying customers. Or you could start the other way around. Find a few paying customers and build something that's worth their money.
I think this is something where many startups struggle. It doesn't matter how good you feel your product is unless it has some value in the real world. Starting with a customer gives you an edge. You will really have to provide some tangible value to make people exchange their money for your service.
If you can do this with a few and prove that your service is actually useful, you have proven something extremely valuable. It is much easier to scale something that has been shown to work rather than to aim for the masses at first and just hope it will work. You are not going to reach those masses without something really tangible.
I think this is one of the key ideas of Steve Blank's concept of customer development. I ran into the separation between customer and user in Ash Maurya's "Running Lean". It's one of those books that really gives you some perspective and tools to apply in building your business.