In today's Philadelphia Inquirer, a letter writer (Melvin Goldberg of Ambler, PA, stand up and take a bow) complains: 

You did an excellent job covering the inauguration. However, you twice referred to the music played as having been composed by John Williams. Williams arranged it. The composer was Aaron Copland.

Mr. Goldberg is of course referring to "Air and Simple Gifts," a piece specially commissioned for the inauguration:

 Like many Americans, Mr. Goldberg recognized one of the main tunes in the piece, associating it (as many of us would) with Aaron Copland's "Appalachian Spring":

Where our fearless correspondent goes wrong is in not understanding what a composer really does. A composer does not simply "write tunes." If that were the extent of it, then both Williams and Copland were "arranging" a composition by Joseph Brackett, a Shaker elder. It is certainly true that a composer often works with original melodies and themes, but I would argue that the main job of a composer is organizing music, whether new or pre-existing.

"Simple Gifts" brings with it certain associations and connotations that Copland drew on expertly when using the melody in "Appalachian Spring." He could have evoked America with other themes like "The Star Spangled Banner" or "My Country 'Tis of Thee," for instance, but those would have had entirely different connotations. (It's hard to quantify the difference in words, but I bet you can feel what I mean.) When Williams decided to use the same melody in his "Air and Simple Gifts," he could draw on the associations with both the original Shaker tune and Copland's treatment of it. But both Copland and Williams did not simply give a new arrangement to Brackett's music--they didn't just make a "cover version"--they used it as a building block in their larger compositions.

Then what's the difference between arranging and composing? I would say it's a fairly blurry line, but an arrangement would largely retain the structure of someone else's composition, as opposed to merely borrowing a tune for further development. There's also a difference between using music that has universal connotations within a culture, and stealing a good tune to pass off as your own. Modern-day sampling presents a similar dilemma--who "wrote" a song that uses pre-existing music in a new way. Sometimes the sample is used organically in the structure of a song (e.g. see the music of R.A.K.I.M., Atmosphere, or Eugene's Business), while other times the main attraction comes from the sample as opposed to anything the sampler has contributed (I would argue that Kanye West's "Jesus Walks" and "Gold Digger" are good examples of this type).