thunderbolt - hdmi not working

I am no expert but I used to connect my samsung tv via a kanex minidisplay port to hdmi cable..

air play only works if you have something like an apple tv connected to link the tv to the mac or whatever else.... hence the name air play... no wires... if you have nothing of that sort then it wont work.

i have no idea what the other icon is.

if you are saying you are connecting via cable now, then you should turn on your tv to whatever hdmi port you are connected to then you can access the option under settings display... then you can choose to mirror display or extend the display which is what I do.. do I drag my media player to the extended screen and play whatever I want to watch there for example...

but if i am correct these option are only available when you turn on your tv to the correct hdmi connected

try it and report back

** see I just noticed this is in the apple tv thread** are you in the same position I am.. where you used to have a cable, now you are using apple tv? If so to properly configure your tv needs to be on.. to mirror there is no issue, if you want to extend then you need to choose the positioning..also in the diagram there should be a bar at the top of one of the displays.. indicating which one is the desktop...so you see 2 screens beside each other and you want the tv to be on the left so when you move the mouse to the left it goes onto the tv etc.. well you can move the position of the screen to left of right and if you click the top bar that can be moved if you using 'extend your screen' to choose if you want to use your tv or mac screen as the desktop. this might not be a problem for you but for me it went default to the tv and i had to figure out how to fix it..