Is the connector the only difference between a Cinema Display and a Thunderbolt Display, or are there other features that changed between the two models as well?
The Thunderbolt monitor includes a number of integrated peripherals as well as being a monitor:
The actual connector for MiniDisplayPort and Thunderbolt is the same, but Thunderbolt can pass many protocols over the same cable, not just A/V signals.
The panel, power and general design of the two screens are the same, however as Stuffe said above there are additional ports which are powered by the Thunderbolt connector.
There is also an integrated power lead for Macbook (Air/Pro) and I believe it's active power consumption is a little higher.
The Thunderbolt connector is not backwards compatible with a Mini Displayport 'port' - but of course a mMini Displayport is compatible with the thunderbolt 'port'.
Last point - you can daisychain the Thunderbolt display with an additional thunderbolt (or cinema or any other) display using the Thunderbolt output port.