The 'lighter' of the two reset options. It can be done either in settings or via recovery menu. It wipes all user data and firmware settings but leaves the contents of your internal SD Card intact.
Restores a tablet to its basic factory settings, which erases all applications that were installed by the user as well as all user data. Hard Reset wipes everything including the contents of your internal SD Card. Whatever firmware you last flashed will be the firmware you get back, but everything else will be wiped.
Clear? Ok, let's proceed with the Factory Reset of a Google Nexus 7 (2012) from within the menu settings:
Settings > Backup and Reset > Factory Data Reset > Reset Tablet > Erase Everything.
Please remember to back up any data you want to keep first! In the Factory Reset screen you also have the option to Backup My Data, Backup My Account and Auto Restore. These are good options to tick before you Factory Reset if you're not too sure how to do this on your own.
If you're at all paranoid about your SD card contents just take them out before you do the Factory Reset. Attention: if you reset your device to the factory default with SD card encryption setting enabled, the device will not be able to read your encrypted files when you reinsert the SD card. Disable this setting before resetting the device.
Remember sometimes you don't need to go even this far to solve problems. First of all try just turning your tablet off for a while. Sometimes something as simple as that is enough to clear up some simple problems.
But if you've tried all of these methods and are still having problems, you can try a Hard Reset, the instructions for which are here.
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