Super confused here because the distinction seems completely clear to me? Relatively few plants, when mature, will start growing clones up from their roots, but it's a known growth pattern. They're called suckers, and I've never heard them referred to as distinct individuals.

But most plants can be cloned by taking a cutting and giving it continuous water + air and letting it start growing a new root system. I've never heard anybody suggest the cutting is not a new, distinct plant.