iPhone: What is DFU mode, and what's the difference from recovery mode?

In the past couple of days, we've seen reports here and there of iPhones getting stuck in a restart loop. The black screen with the Apple logo shows up, holds for a while, and then disappears again; repeat ad infinitum. While it's not clear yet exactly what's triggering the issue (the complainants suspect that it may be a recent application update to blame), there is a tried and true way to get your iPhone, iPod touch, iPad or older iPod back to square one: either use recovery mode or do a

Cheap iPods