Those four lists—Playlists, Artists, Songs, Videos—are only suggestions. On a real iPod, of course, you can slice and dice your music collection in all kinds of other listy ways: by Album, Genre, Composer, and so on.
You can do that on the iPhone, too; there just isn't room across the bottom row to hold more than four list icons at a time.
To view some of the most useful secondary lists, tap the fifth and final icon, labeled More. The More screen appears, listing a bunch of other ways to view your collection:
Albums. That's right, it's a list of all the CDs from which your music collection is derived, complete with miniature pictures of the album art. Tap an album's name to see a list of songs that came from it; tap a song to start playing it.
Audiobooks. One of the great pricey joys of life is listening to digital "books on tape" that you've bought from Audible.com (see Audiobooks). They show up in this list. (Audio books you've ripped from CDs don't show up here—only ones you've downloaded from Audible.)
In a hurry? You can speed up the playback without making the narrator sound like a chipmunk—or slow the narrator down if he's talking too fast. iPod has the details.
Compilations. A compilation is one of those albums that's been put together from many different performers. You know: "Zither Hits of the 1600s," "Kazoo Classics," and so on. You're supposed to turn on the Compilation checkbox manually, in iTunes, to identify songs that belong together in this way. Once you've done that, all songs that belong to compilations you've created show up in this list.
Podcasts. Here are all your podcasts (Podcasts), listed by creator. A blue dot indicates that you haven't yet listened to some of the podcasts by a certain podcaster. Similarly, if you tap a podcast's name to drill down, you'll see the individual episodes, once again marked by blue "you haven't heard me yet" dots.