It’s complicated! The size of the tyre matters but what arguably matters more is the shape of the tyre. You’d think a carcass would be circular in cross-section but when the tread is moulded onto it it can take a more squared off shape. And more importantly the tread blocks themselves change the shape of the tyre. So the High Roller below is a squarer tyre:
Whilst the Trail King is a rounder tyre:
Put a High Roller on a very wide rim and it’ll roll much more slowly, corner nervously on harder ground and be difficult to tip into turns on loose ground (though it will bite well once it’s onto its edge). Put a Trail King on a narrow rim and it’ll be prone to squirming unless at very high pressures and will struggle to find any sort of bite when cornering.
What complicates things further is that the Trail King has a lot of carcass volume compared to the tread width so it won’t suit a super wide rim – for that you want a tyre which is relatively shallow of sidewall and fairly round in profile like a Minion DHF:
But go too wide and that’ll end up too square…