The gold displayed in the Raid Loot screen is the total amount of gold you get from raiding those nodes; the game then uses that gold to pay for crafting the badge and its various sub-badges. If the cost of crafting the badge is higher than the amount of gold you get from raiding (and it usually is), then you’ll have to pay extra from your inventory, which is the amount shown on the Power Craft screen.
There’s a series of screenshots of someone crafting a badge here, and the next comment goes into detail on exactly what happens with the gold, if you want a fuller explanation.