Donald "Beezer" Smith is either the brother of Jay R. Smith or Wheezer Hutchins. While a boy named Wheezer turns out to Jay's brother in Rainy Days, there is no sign of Beezer in that short. While Wheezer and Beezer are the brothers of Mary Ann in Little Mother, he never again appears as a sibling to them in their family history through the shorts.
Conceivably, there is a possible behind-the-scenes scenario that the Hutchins and Smiths are related, but the on-screen facts would refute this.
Whether siblings or cousins, Wheezer and Beezer are seen as close friends for the short appearances they have together. They are seen sharing a sandbox together in Fair And Muddy and in the audience of Joe Cobb and Chubby Chaney's boxing match in Boxing Gloves. When Wheezer rescues all the animals in town in Cat, Dog & Co., Beezer is right there helping him.