ETH smart contracts v/ traditional total newb here. 

I purchased some ETH on an exchange which uses smart contracts, it is in that exchange wallet.  I have another wallet which does not support smart contracts, only "traditional" ETH transactions.

Apparently the ETH is not transferable between these 2 wallets.  I am trying to find information about if it is possible to transfer ETH from a smart contract wallet to a "traditional wallet".  Is this possible?  Is there a way I can convert the smartcontact ETH back to "traditional"?

If this isn't possible then it seems smart contract ETH and "traditional" ETH aren't even the same currency anymore.  Is that the case?

I have put "traditional" in quotes because that is the term i've seen although i don't know if that is a correct term.
ETH transactions between "smart" contracts and "dumb" wallets are always possible. The fact that your wallet does not support smart contracts does not mean you cannot send funds from a smart contract to your wallet, it just means you cannot manage a smart contract from said wallet. You can still send funds back a forth between the two.