The apostrophe in "boy's dog" is not a contraction. It is possessive indicating whose dog it is. You wouldn't use a contraction with a word like boy. You would, for example, say "it's" as a contraction of "it is." Å ha is "to have." While "the boy has a dog" and "it's the boy's dog" convey more or less the same information, the former is giving us information about the boy and the latter is information about the dog. Hope that makes sense.