The American term means HD-ready needs an external tuner to tune broadcast HD - the internal tuner is SD only, while Full HD means that the built in tuner can get broadcast HD. Specifically for sets sold in the middle 2000s when those terms were uses there, is that HD-ready had NTSC only tuner, and full HD had ATSC digitial - which ATSC by default supports HD. In the UK it is a bit different, as TVs have for some time supported DVB-T digital, but only in SD. They need DVB-T2 to support HD.
In British retail parlance as I see it, it seems HD-ready is 720P native, Full HD 1080i/p native, regardless of tuner capabilities.