Are all the short messages we send now sent through the website? Or is it sent by mobile or Unicom operators?

If you are talking about a short message sent from a mobile phone to a mobile phone, such as you send it to a friend, this short message is a peer-to-peer message, which is sent from your mobile phone to a friend's mobile phone through the operator's gateway.

All short messages have to go through the operator's gateway, whether through the website or in other ways.