This question confuse many newbie alot and i want to take a little time to throw more light on this topic. As understanding the difference between these two may help you secure your wallet and enable you know when to use one against another.
What Is Myetherwallet ?This is a user friendly interface that allows you store, receive, and send ethereum token and all standard ERC20 token on the ethereum blockchain.
You need the Un-disclosable private key to get access to Myetherwallet to be able to carry out any of the features(transaction) above. And for all ERC20 token it requires you to manually add those token using the token Contract address, ticker and decimal.
What Is Etherscan ?Etherscan is like a mirror to ethereum blockchain. It mirrors all the stores token on an ether wallet, it shows transaction history of sent and received token, and available token(Standard ERC20 Token) on your wallet.
It is used to look up your wallet for transaction history. You can say its more like an ethereum search engine (Google search the web), (Etherscan for Ethereum blockchain). To be able to view your transaction history all you need is to input your wallet
Public Key. Viola! you can view all your assets and transaction history.
The DifferenceMyetherwallet is used to carry out transaction(send and receive) while etherscan is used to search and view all transaction on the ethereum blockchain using your Public key.
You can check out my other thread on
How To Stay Safer With Your Private Key and Secure Your Crypto Assets https://bitcointalksearch.org/topic/m.40647747