I'm presenting a talk on troubleshooting OS X and iOS for a Mac user group next month, and I was surprised to hear that several members thought a "hard reset" or force restart of an iPhone or iPad is a useful troubleshooting procedure. They suggested that it does some sort of clearing of caches or resetting of [insert hand waving here] which is different from simply shutting the device off and turning it back on.
I've searched pretty deeply across Apple's support site, the Apple discussion forums, the popular Apple news websites, and sites offering Apple tech tips and I haven't found any corroboration.
To clarify the answer I'm seeking, I'm particularly looking for firsthand knowledge (i.e. "Apple told me a force restart does foo") or a published reference that confirms one way or the other.