Electrum only offers online wallet, does it not? I am currently using Bitcoin-Qt and have just surfed to Electrum's website.

It seems that Electrum only offers an online wallet, not offline. Is that correct?
No, electrum only offers offline wallets.

I think your confusion comes from electrum being a thin client. But this only means that electrum does not download the blockchain, instead it uses a server to query for the the information it needs out of the blockchain. From the elextrum bitcoin.it Wiki page:


  Main features:
  
  
  ...
  Instant on: the client does not download the blockchain, it requests that information from a server. No delays, always up-to-date.
  Transactions are signed locally: Your private keys are not shared with the server. You do not have to trust the server with your money.
  ...