As far as I'm concerned, a power armor is a powered exoskeleton covered with armor plating whereas a cyborg is an organic being augmented with inorganic modifications, with a degree of permanence - said enhancements are not necessarily completely irreversible, but installing or removing them generally cannot be done on the spot - so for instance if you have machine interface installed and you use it to control a drone, you can sever contact with the drone at any time, meaning the drone is not a cyborgization, but the machine interface itself must be integrated with your nervous system, which means it would take advanced surgery to install or uninstall, making it a cyborgization. In the case presented, I guess I'd consider it to be a cyborg with a lot of external plating, though should the life support and exoskeleton be capable of autonomous action, it'd probably be more of a power armored cyborg (which is very common, as many applications of power armors in fiction take advantage of machine interfaces). Or, if removing the life support system, even if lethal for the subject, could be performed without invasive surgery, it'd be a specialized medical power armor, I suppose?
Edit: From a writing standpoint, how much does it even matter? It's not like real world has seen very significant advancements in either cyborgization or powered armors, so those definitions are still fairly malleable and ambiguity in this regard could provide fodder for some interesting internal conflict/crisis of identity. Or you could play it for laughs, maybe even try and squeeze a badass oneliner out of it, maybe something to the tune of "". Anyway, good luck and have fun writing!