During the Prison Pete random event you are supposed to catch at the least 3 of these to obtain the prison key which resides in them. However, you must pull the lever beside the barriers to get an image of the specific type of Balloon Animal you're supposed to catch. Once obtaining the key from the corresponding animal, you are prompted to give the key to Prison Pete, who then attempts to open up a barrier. If it is the right key, a barrier is taken away (there are 3 barriers), if it's a dud, the barrier will not disappear, or if there is already a barrier taken away, it will be replaced with another one.
The varying characteristics between each Balloon Animal can be easily distinguished from their horns, body width, and tail length.