A television set with the "Full HD Ready" marking means that the display is capable of displaying 1080 lines at 24, 25 and 30 frames per second (not using "interlaced" mode). This usually means that the resolution of the screen will be 1920x1080, about 2 megapixels. This is the "Full HD" bit.
It also means that the display device has a suitable digital input, such as HDMI or DVI to provide the pictures to display, this is the "Ready" bit.
I find the whole HD TV scenario confusing and I suspect many people do. I have a perfectly good TV system consisting of a plasma TV ( apparently HD ready) and a HUMAX FREEVIEW PVR. This was quite expensive but is reliable. When FREEVIEW introduced HD transmissions it appeared it was going to be an extra service. But recently I notice that at least one Freeview channel - Al Jazeera English - has moved to HD and no longer is available to those of use without HD equipment. I am assuming that this now going to happen with other main FREEVIEW channels ie the various BBC, ITV and Sky News channels thus effectively forcing viewers like myself to buy expensive new HD boxes and TV sets if we want to use FREEVIEW. In the computer industry backward-compatability is fairly common - ie much effort is put into ensuring that updated standards or systems do not instantly make users equipment useless. I wonder why the HD standards were not designed to allow older equipment to stll use the new transmissions (though obviously at lower definition).
The problem has been created by marketing departments using the term 'HD Ready' to indicate that the screen is capable of displaying HD pictures. It does *not* mean the TV set is capable of tuning in to HD transmissions though. It is that factor that causes the confusion and is typical of marketing not having thought through the related issues.
TV sets that have a DVB-T2 tuner, and so are capable of tuning in to HD services, *are* backwards compatible with non-HD transmissions - that is what backwards compatibility means in this and in computer terminology. (In the computer world, the release of Windows 10 has caused many people to have compatibility problems as their equipment is not capable of running W10 and many of the drivers needed to able to work with W10 are not available at all. So W10 is *not* backwards compatible' in your terms.) I suspect what you seek is 'forward compatibility' but that can never be quaranteed as new methods of transmission and encoding cannot be predicted.
(Another example of things that are not backward compatible is the change away from leaded petrol. Many older cars were not designed to run on unleaded and where possible need to have major modifications to the engine, particularly the exhaust valves and seats. Additives were available but have been withdrawn.)
The simple solution is to retain your current TV set and connect an HD capable 'set top box' and use that instead of the SD tuner in the TV. Alternatively, you could consider replacing your energy hungry TV with a modern HD capable (not just HD ready) that means fewer cables and uses considerably less electrical energy than a plasma set.
MikeP: Entirely agree - an HD set top box is an easy solution, which is what I did. They can be had for as little as 43 pounds in the high street (although I must admit that my Manhattan does play up, so I'm not sure I'd recommend it). The alternative is to kill two birds with one stone, and get a new Humax. The latest one will have 3 HD tuners, have Freeview Play (so you can scroll back and even record from the last 7 days), get all the on-demand stuff from the four main channels, and is wified. About ?200.
And yes, a new TV 'should' have an HD tuner as standard. Of course plasma does have lovely black levels, and its just the tuner that could do with being upgraded, but your right Mike - you can heat your front room with some of them!