Apple - Does a force restart in iOS do anything different from a normal restart?

A force restart is at the hardware level, not the software level. This means that even if iOS is completely frozen or in a different mode altogether (such as DFU Mode, Recovery Mode, or Restore Mode), you can still perform a force restart. It does nothing more than cut the power and turn the device back on again. This means that it doesn't clear any caches or reset anything. A regular restart actually does more than a force restart.

The "Hard Reset" is a useful troubleshooting feature, because it's very often the only way to restart an iOS device that's malfunctioning. Normally it isn't advisable to do it for the same reason as on a Mac: it may cause corruption. But it's definitely a useful thing to know how to do for the times you need it. It actually does less than a regular restart, because it prevents the OS from following normal shutdown procedures. Not a great thing to do on a regular basis and there are better ways to force a filesystem check of the device without potentially causing data files to be left in an inconsistent state.

You might find this article by an Apple employee useful:

http://www.payetteforward.com/how-to-hard-reset-iphone-why-its-bad/