Welcome to Android Central! I always considered a hard reset to mean the same as a factory data reset. Turning the phone off and then on would be a "hard reboot" to me.
If you want to do a factory reset and can't get to the main Settings>Backup & Reset menu, then try powering on with Power, Vol Up, and Vol Down all pressed at the same time. Does that give you a Recovery menu with a Wipe Data/Factory Reset option?