Difference between hard reset and factory reset

A hard reset is just getting it to restart when it's otherwise stuck in some loop where the normal (software initiated) restart doesn't work, or one can't seem to get any response. It could be something just locking up where everything is really slow and the user would just like to start over.

A "factory reset" (Apple calls it a "factory restore" is just getting the operating system to a condition similar to an iPhone right out of the box. It's possible to do that with just an iPhone alone. The idea would be to wipe out all data and settings. I don't believe that method requires connecting to internet. But there are other ways, such as using a computer, where it will load the latest compatible version of iOS and can even restore it if the operating system setup is corrupted and not working.

Apple just uses these two correct procedures names:

• Force restart = Force restart iPhone – Apple Support (no internal data affected)
• Restore to factory settings:--> Restore your iPhone, iPad, or iPod to factory settings – Apple Support (this erases all data on the device, except the operating system)

Regards

Giulio