Judging from the fact that you are new enough to ask the question, it's seems you'll benefit most from a very over-simplified answer....so here goes....
1: GPU BIOS UPDATE - This is used to program the actual bios chip on the card.
DO NOT take flashing/updating the GPU bios lightly!
If something goes wrong during a bios flash/update it can damage your card!
Since it programs the actual chip on the card itself, restarting/rebooting your pc will not fix the problem if there is one.
So as a general rule - flashing/updating a bios of any kind be it GPU bios/ motherboard bios etc..etc.., should not be done by new users until you fully understand the risks involved.
2: Asus GPU tweak - This is a program used in windows to fine tune the performance of your card.
It is generally used for overclocking your GPU for better performance.(but can be used for other things such as undervolting etc...etc..)
GPU tweaking programs are far more new user friendly since they are programs that only change settings once windows loads the software and applies the settings to your card, so the changes are never "permanent" to your card like a bios update is.
So if you screw up, you can just undo the settings and/or reboot your pc or simply uninstall the software to return your card to it's default settings.
But that does NOT mean you can't damage your card with software tweaking!
Care should ALWAYS be taken when overclocking a GPU especially when playing with voltage settings.
It's best to spend some time gathering info and fully understanding what you're doing before attempting to tweak your GPU for better performance using a GPU tweaking program.
As I said, this is a VERY oversimplified explanation and is just meant to help you understand the difference.
I hope it helps. :thumbsup:
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