JMO if you found them on a know site then I would lean toward artifacts. The 1st one almost as the look but not quite. If you were grinding something over a long time your grinder would get a rounded shape and not have a dip in the center or square edges. The other stone I'm going to say natural but keep your head down and your eyes open and you will find something.
I believe there were some pestles made with a convex area. My understanding was they didn't want to crush the seeds some of the berries contained. They could reduce the berries and not crush the bitter seeds.
Quite a few Pestles will have that small indentation on the bottom of them. That could very well be a Pestle. Could you take some better pics at different angles of the first piece? I think the 2nd one is natural.