what is the difference between digital and HD broadcast?

Tell you the difference ‘technically’??
I can tell you as a layman that digital is the signal and hd is the format.
Soon all TVs in the UK will receive a digital signal, no big deal, and very little cost to you.
Now recently my big old fat TV was on the blink, I had read all about this new HD thingy, all these ‘technical’ experts were telling us how great it all was, fantastic improvement in picture quality etc etc.
I already had a dish and on sky so I bought a digital TV HD ready , nice slim line thing big screen great picture, I am happy with it.
So the other thing on my mind was HD that must be really great if it can even improve what I now have????
In the UK we dont have any HD broadcasts except via sky TV about £250 for a little black box then an extra subsciption of around £10 a month.
OK I still wanted to see one in action, if it could improve the great picture I have now it must be great???
A trip around all the stores , a simple question, "Could you show me a working TV with a HD picture on it please"????
No chance!!!!!!
Then just today I was wandering around my local ASDA store they had a sale HD DVD player under £30, I went to have a look at one it was connected to a HD TV all the correct cables and it was playing a HD DVD , I looked at the picture quality , nice big slim screen the picture was absolut cr*p!!
I called the ‘technical’ guy over, I asked "was this a HD picture on the screen"? He assured me it was, in fact he added "great picture isnt it"???
They can stuff it for me!!!!
End of my ‘technical’ report