Press the power and volume down buttons at teh same time .. it does a hard(er) reest.. phone comes up again
The term you are looking for is a 'soft' reset.
Soft reset (Power + Volume Down for around 15 secs until phone vibrates) performs pretty much the same action as disconnecting the battery and then reconnecting it. It simply reboots the phone and causes the operating system to restart. No data, settings or apps are lost.
Hard reset (Settings > About phone > reset or Power + Volume Down + Camera Button for about 15 seconds, then lift finger off camera button and follow onscreen instructions) completely resets your phone to its factory defaults, deleting your personal data, settings and downloaded apps. After doing this you will need to setup the phone from scratch again.
Turning off the phone (pressing the Power button for a few seconds and then swiping down the confirmation screen) should do pretty much the same thing as a soft reset, so I'm not sure why some people are getting different results with this. Perhaps someone else knows if there's a difference between a soft reset and a normal power down (other than powering down doesn't restart the phone straight away and can't be used if the phone has frozen).