I think it's the second. Even on No Man's Sky, with the bazillion worlds, they all exist "as they are" and are consistent from the beginning. If you revisit a planet, it's exactly as it was.

Now with what I know about this technology, I suspect the way this happens is every planet had a seed (a number) that you can pass to the "random planet generator" it will generate exactly the same thing over and over. Then basically when you load a new planet it goes "right, with this seed, what would we have in these coordinates?" And the answer is persistent.

However having seen how that looks in NMS, I feel they'd have had to add a bit of extra spice to be able to sell a single world. In my mind that involves manually crafted areas almost necessarily, as well as checking most of the planet manually to oversee the procedural generator and massage anything that doesn't pass a level of quality. If I were to make this game myself, I would use procedural generation for the different areas and not for the whole planet, so that I can give certain sections of the map a "reroll" if I don't like them.