The term 'Wrinkled Dog' can refer to two different breeds of dogs: the PUG and the Sharpei. The PUG is a small breed of dog with a wrinkled face and a curly tail. It is known for its friendly and playful nature. The Sharpei is a medium-sized breed of dog with a wrinkled face and a short, smooth coat. It is known for its loyal and protective nature. Both breeds are popular companion animals and make great family pets.