After I sign in, here is what I see:
In the above screenshot you see the Messenger window layout on a web page. It has the contacts in a list on the left side, with the orange indicators for the ones who are available. Then, if you click on a contact, a new window opens up on the right hand side in a tabbed format, one tab per contact you are chatting with. This is a nice interface as it keeps all the conversations nicely tucked away in tabs. The nice thing is that I can use it anywhere and I do not have to depend on the standalone version.
On the other hand, the other popular chat program, MSN Messenger has a similar web version for a long time now. The MSN Messenger for the web opens up as a popup window and looks exactly like the standalone version except for the tabs on the left.