Underfloor heating with wall heating in a wood-clay house

what is the difference between solid wood and full wood?

Full wood is what the layperson imagines when they hear "solid wood": wood as it is sawn from the tree - processed as it grew. Full wood is therefore always also solid wood, but not vice versa: solid wood can also be joined, for example glued laminated timber, finger-jointed wood or plywood. Just as "form ham" did not grow on the animal in the form it comes to the plate, but is otherwise "completely genuine."

Why is full wood not sustainable?

Because it was sawn "in one piece" from the tree in the desired shape. Sustainable forestry involves the market taking the wood that is available - that is, not additionally cutting wood from which one can saw out "monolithic" desired pieces. In addition to storm wood from recent decades, currently a large amount of beetle-damaged wood is being harvested, meaning the vast majority of the trees felled now would naturally not yet have been ready for harvesting and are in a sense "premature". But you cannot saw thick long beams and panels from trees "slaughtered as calves". At the same time, advances in wood technology over the last fifty years allow for equally load-bearing and otherwise durable constructions from joined wood, as were known only from solid wood in grandfather’s times. Solid wood that is not at the same time full wood is therefore decidedly more eco-bio-sustainable, even if the average layperson is still stuck in old times. We used to have an emperor, Uncle Alex used to say (but that was also when the Ergo Group was still Hamburg-Mannheimer). Panta rei, tempus fugit - also in carpentry.

Oh, that's what you meant. Thanks. Yes, of course you have to deal with the wall structure and choose a system. I hadn't really thought of log beams for solid wood because that is usually referred to as a log house. But even that is definitely much more sustainable than concrete. And it is also very much a matter of taste for a few interested parties.

With system wood/cross-laminated timber, you can build 'normal' houses for everyone. Facade and interior plaster as desired. Whether the wall structure uses glue, screws, or wood screws can still be discussed. Everyone has to choose "their" level of sustainability.

A modern underfloor heating system has such low temperatures that the tiles don’t really get warm, so there’s not much difference to cool.

That’s not really the case. At our place, the heating was on for one night at the beginning of October, and feet definitely feel much more comfortable on the tiles then.
Bare feet on 20-22°C stones simply aren’t pleasant.
With wooden floors, however, the effect is not as pronounced.
If a screed is planned, I would always include underfloor heating. If you have plank floors or just a solid wood floor or similar, the decision is more difficult.