You can definitely use the same keys. You cannot actually send ETH to ETC or vice versa (if I hand you a US dollar, even if you were expecting a Euro, it's still a US dollar). It looks like you sent ether on the ETC chain in Polloniex. To regain access to this ETC, open an ETC wallet program and import the keys created by your ETH wallet.
In theory (or at least for the purposes of this discussion), every Ethereum address has a key that unlocks it. When you "create an Ethereum address", you're really generating a secret (private) key and then figuring out which account it unlocks. Since the same keys work in both the ETH chain and ETC chain, when you generate an Ethereum account key, it unlocks both accounts. Since all accounts start off as empty, if you look for your account balance on the wrong chain, you'll see it has no ether.
Thus, you should think of your address (and account) as an Ethereum address (and account). The keys for all Ethereum accounts unlock ether stored in the Ethereum Classic and Ethereum (non-classic) chains. However, the amount of ether each account contains depends on which blockchain you check. When you sent ether on the ETC chain from Poloniex, the Ethereum account with the address 0x407e1bb8b5c114e40469eedb5632518b68f9be38 on the Ethereum Classic chain was credited with 7.49 ether. Since it's on the Ethereum Classic chain, we say that you sent 7.49 ETC. No ether was sent on the Ethereum (non-classic) chain, so 0 ETH was sent. If someone sent you an ether on the Ethereum (non-classic) chain, then the key for the 0x407e1bb8b5c114e40469eedb5632518b68f9be38 account would have access to 7.49 ETC and 1 ETH. So you need to export the keys you generated in your wallet that sends and receives transactions on the Ethereum (non-classic) chain. Next, you import the same keys into a wallet that is sending and receiving transactions on the Ethereum Classic chain.
For example, you can see that account 0xdf15b90591fcfc3f313291c6c1fdedc2f2b34373 has ether stored in the Ethereum Classic chain and the Ethereum (non-classic) chain (and the transactions list and final balances are different, too).