The trading systems in which auctioning is most prevalent are indeed greenhouse gas variants of cap and trade. When a government establishes a cap and trade system, you have to decide who gets permits and how to issue the permits. Do you issue them for free, sell them for a fixed price, or do you auction them?
From a pure market perspective, auctioning certainly has some advantages. I'm not suggesting that's the way a government would necessarily go, but many jurisdictions have chosen to auction at least some of the permits, because that allows the market to demonstrate the value of the permit. The person who needs it the most will pay the most.