There is a useful distinction between the creative modes of composing and arranging. It is easiest to think about with music. A composer is someone who creates a new song. An arranger is someone who takes an existing song and gives it new life. These two modes apply to any creative act, and each person tends to be dominant in one mode over the other.
More generally, a composer is someone who creates something novel. It is something of its own accord. Something that wouldn't otherwise exist if the composer didn't sit down and make it up. An arranger is someone who takes an existing piece and puts it together in a new way. This might mean coming up with a better version, or a version that brings out different qualities. It might mean presenting something in a context other than the one in which it was originally developed. Whereas the composer brings something into existence, the arranger gives something an existence it wouldn't otherwise have.
Composers tend to be recognized for higher artistic merit. A composer will often toil in obscurity for long periods, because the value of what she's created is not yet recognized. Something that's new is by definition something that doesn't fit into existing schemes. People won't know what to make of it or how to use it. For example, even if you haven't studied music history, you can probably name quite a few famous classical composers off the top of your head -- Bach, Mozart, Chopin, etc. But how many of them are living? Very few, if any. Often, successful composers are not recognized in their lifetimes. The same is true of art history. Many of the artists who composed a new means of representing the world were not lauded while they were still alive. A famous example of this would be van Gogh.
Arrangers tends to get their payoff much earlier. There are several ways this payoff can come. Often times they make more money. In many cases the arranger is a salesperson. She's found a new way to present an idea or product, or has found a new market to which she can sell it. Sometimes this is behind the scenes. After all, how many famous musical arrangers can you name? But sometimes it's out in the open. When it's out in the open, it's usually because the arranger has brought an idea or product to a larger audience. The larger audience gives them the credit. But the more discerning niche audience for which the thing was originally intended looks down on the arranger as a mere popularizer.
A classic example of an arranger is the writer Malcolm Gladwell. He takes ideas that already exist and arranges them in new and engaging ways. How many ideas has Gladwell actually come up with on his own? None. Yet there's power in what he does. It is a process of taking the best ideas from obscure areas and delivering them to a much wider audience. And when he makes an idea his own, he does it in a way that gives it a life it would not otherwise have. The tradeoff is that he's often derided for not knowing what he's talking about. It's easy to target him for not having the same merit as the composers on which he's drawing.
The flip side of this is that academics are usually composers. They are in the business of pushing the boundaries of known. They bring an idea or finding into the world that wouldn't otherwise be available. In the long arc of a career, this can bring them fame, recognition, and even sometimes money. But in the short term, their work is read by few people and understood by even fewer. For the greatest writers, thinkers, and scientists, their achievements often cannot be fully contextualized until late into their career or after their death.
These two modes also describe different strategies for developing products in a business. A composer creates a product that doesn't yet exist. The technology might be new, as could the problem it purports to solve. An arranger takes a product for which the idea already exists and either finds a new use-case or offers it to a market that's not yet been availed of it. Both are potentially lucrative strategies.
As my friend Stephen Turban pointed out, economies can also behave as composers or arrangers. In the technology industry, the United States tends to an economy of composers. This is where new products come from: smart phones, search engines, social media. On the other hand, the Chinese economy tends to specialize in arranging. Smart phones, search engineers, social media: each of these has been co-opted and optimized in service of a very large new market. Of course, the Chinese production wouldn't exist without the American invention. But as industries come to break less ground, the arranger's skills become more valuable. American manufacturing has suffered for many years; that kind of business has shifted to places like China.
A similar effect can be seen in education. Asian countries, like Korea, tend to teach a rigorous form of arranging. Their students learn material better than anyone else. The extent to which they do this is the extent to which they succeed. In the best case scenario of the U.S. system, students are encouraged to do something closer to composing. It's not just about comprehensively digesting the most material. There is also room to bring something new to the table. In this case, I'm not sure the metaphor holds one-to-one. But it is still perhaps worth considering.
The main utility in drawing this distinction is that it allows the creative to draw a clearer line between what she does and what she doesn't do. If you're an arranger, it's not your responsibility to be original, to be artistically venerated, or to worry about whether the hipsters think you're cool. If you're a composer, it's not your responsibility to succeed right away, to do something that's of obvious value to everyone, or to scope your work for a the broadest possible market. The trick is to find the right mix of the two that works for your creative process, and to trust in the value -- whether it's realized in the long term or the short -- of what you're making.
Composer. Arranger. Either one has its pros and cons. The key is to be the one that better suits you.