Full HD should have a HD tuner of some sort built into it (either freesat HD or freeview HD) so it should be able to receive HD with no extra boxes.
TV's that need an extra box to receive HD are generally called HD ready.
However... there is a lot of confusion on this matter and often sales staff in shops get confused about it and give out misleading information, so it's always worth double checking the specs on the TV you are looking at yourself.
Unless it very specifically says 'HD tuner' (or possibly 'T2 tuner') it will not receive HD programmes from freeview or freesat.
As chuck says, there is huge confusion on this matter - 'Full HD' does not guarantee an HD Tuner, it merely refers to the maximum resolution of the screen display.
It is actually possible to have a 'Full HD' set that does not have a digital tuner of any sort built in - merely an hdmi input that will accept HD signals.
That one seems not to have an HD tuner in it (which buggers up my answer somewhat :) )
I wish they would standardise this... my TV was advertised as HD ready but it is a full 1080p TV, but has no HD tuner... I've seen others advertised as full HD that are only 1080i but have a HD tuner in them!
I am sorry if I have dished out (no pun intended) wrong information, I speak from the experience of having just bought a Panasonic TX-L32EW5, and have no problem with watching both normal and HD transmissions. Before settling for that model I looked at maybe a hundred sets by various manufacturers all working in HD in a large showroom [Saturn/Germany] and none required, nor was it suggested to me that they required, any extra equipment.