This stone was cut but not polished to show the coral pattern that is hidden inside.
When you wet it you can see the coral pattern more clearly. Often these stones are polished and used for decoration.
The piece above had been washed and naturally tumbled by the surf of Lake Huron. Here is very good example of what a small intact colony looks like without the tumbling.
I'm not sure which formation any of the above specimens came from. The "Petosky stones" were beach float while the colony was unlabelled save for "Michigan, Devonian". They all most likely originate in the middle Devonian (Givetian stage).