A Thunderbolt port can be attached to an HDMI TV via a Mini-DisplayPort to HDMI cable...Apple does not make that cable but does offer them for sale. I bought one last Saturday at an Apple store, Kanex Mini-DP to HDMI 10 ft Cable, Part Number H4637ZM/A, $44.95. I was uncertain about how this would work with the TV so I also bought the Apple Mini DisplayPort to VGA Adapter-INT, Part Number MB572Z/B, $29.00 just in case.
The cables connect to the Thunderbolt/Mini-DisplayPort, and you then have to select System Preferences > Display and use Mirroring or not according to how you want to operate. That should show up under Displays and the Arrangement button top center of that window.
There should be only one Mini-DisplayPort configuration since it is an Apple thing...same port as Thunderbolt, but third-parties may not be correctly identifying their cables.
Give the Apple store or on-line store a try...what they sell will fit.
for FAQ info on the ports and adapters.