We need to see if the rock you're holding has a sharp bit, like an axe would have. Can't really tell from your photos. If one end is tapered to a bit, then it would be a celt. Even if not sharp, but made blunt from usage. But we need to see if it tapers at one end....
The bottom one is not a mortar or a grinding platform. The reason being is they would not use a rock that was cracked.Looks like a lot of the rocks out of the Tennessee river down in Ala. River cobble.