This one has an imprint in it that looks like a deer hoof. Not sure how clear it is but that's what it looks like.
Another pudding stone
Your "pudding stone" appears to be some sort of conglomerate. The imprint that looks like deer hoof print is likely where a larger pebble (or two) got eroded out, leaving an impression that was rounded and smoothed off with time.
I have some that are pretty big. My husband loaded them wit the tractor and placed them in the yard wit the fork lift. Iam a very big fan of pudding stones myself. I have been toying with the idea of building a wishing well from some of my collection of smaller stones.