Trinity question: what does to subsist/subsistence mean?

In trying to understand various trinitarians theologians like Karl Rahner/Karl Barth, the concept of "subsisting" often comes up. I'm really not sure what to make of it, initially I imagined it means (because of the "sub" prefix) what is the substance something is made of, or more likely a quality of an entity that exists within. But I'm really trying to wrap my head around what's the difference between saying: 1. There's one God who subsists in three persons 2. There are three persons who subsist in one God. Does the first affirm that there really is only one God, as in one person, who inside lives as three? And then the second to mean that there really are three distinct persons, but who inside live as one? Because my trinitarian theology is more western, I'd appreciate (and I've tagged this question) for Catholics and Protestants – as, again, that's what I'd wish for – but Eastern-Orthodox are also welcomed to respond as long as they keep my background in mind.