A "Buddy stick" could refer to a stick that is a favorite chew toy or plaything for a dog named Buddy. It could be any type of stick that the dog enjoys chewing on or playing with. Some dogs have a preference for certain types of sticks, such as those made from a particular type of wood, or sticks of a certain size or shape. The stick could have been chosen by Buddy's owner, or it could be a stick that Buddy found and chose for himself. In either case, a "Buddy stick" is simply a stick that has a special meaning to the dog and is used for play and/or chewing.