I believe that they are concrete sleeve anchors, something like these†. When you screw the nut on and tighten it down, it pulls the anchor in and tightens the expanding sleeve against the hole. With no nut, there's nothing threaded down in the hole so the threaded rod just spins.
I don't think you can pull those out, as the end in the wall is bigger than the sleeve that goes around the rest of the threaded rod - that's what causes the sleeve to expand.
To remove, I would think that you would have to pull it out as far as possible, cut it off, then push the remaining rod back into the wall and patch over it.
You might be able to put the washer and nut back on, tighten them down, cut off the exposed rod past the nut, then remove the nut and push the remaining rod back in. I'm not sure which method would enable you to cut the most rod off.
†Just a convenient link, no recommendation of the store or brand intended or implied.