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:
- 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.
That is not correct.
You can run Electrum on an offline computer, make transactions and pass them to the online Electrum (MPK) to broadcast them to the blockchain.
Electrum has lots of useful options, so you better read about them in the website.