Okay
Let's say I'm sitting here with a video card that requires "2 x 8-pin" power input and comes with a "2 x Dual 6-pin to 8-pin cable"
My computer has inside of it a "SuperNOVA 650 G2 650W 80 Plus Gold"
Can I plug the former into the latter? Trying to know BEFORE I open the box
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You only need VGA1 which splits into the 2 sets of connectors you need. VGA2 is for powering a 2nd GPU. In theory, you could mix connectors from both for 1 GPU but it's not what they intend for you to do.