MyEtherWallet is different from other traditional web wallets.
Why? Unlike other web wallets, here you control Ethereums private key on your machine.
It is an open-source wallet with no third-party servers wherein you can also write and access smart contracts. I have written an article about this here. It has an inbuilt BTC to ETH (and vice-versa) swap facility. You can also connect your Trezor or Ledger Nano S to access your funds in MyEthers browser environment.