You can update the others as well, if they are not the latest, but the VGA drivers are your video drivers, and we're trying to fix a video problem here
As for "How can I tell?":
In the bottom picture, it has VIA/S3G ... IGP - this stands for Integrated Graphics something-or-rather... So then we're looking for a motherboard make/model...
Up in the top picture, we see P4V8X-MX, a Google search reveals this is an ASUS motherboard, so I checked out the ASUS support page for the right link.
It's as easy as that
IGP = Integrated Graphics Processor.