Most of the lab processes are at least structurally similar to that "natural" process: at the end of the day it is just ways of pressuring Carbon into a grid. Maybe a better analogy is that we don't (currently, at least) make a distinction between "natural" foods and "greenhouse/hydroponically grown".
Not exactly. GMO foods are genetically different by definition. Whether or not the difference is significant is another question, but natural vs "synthetic" diamond really is closer to the question of where a plant is grown, or perhaps if it's wild vs. planted.
