They're the same, meaning belonging to the subject. The only difference is that they need to agree with their object.
Use sin for singular en nouns, sitt for singular ett nouns, and sina for plurals: sin hund, sina hundar; sitt barn (sing), sina barn (pl). They are the third person reflexive possessive pronouns, if you want to get technical. They are the possessive forms of sig (which comes in later lessons), and analogous to min, mitt, and minas.
Hounds is only a subcategory of dogs in modern English (large dogs used for hunting). Because of this 'hound' is not really synonymous with 'dog' and I guess it's not accepted because of this even if it has the same origin as 'hund' in Swedish. I can't imagine any native English speaker telling that they have for example a Chihuahua hound (even if this would've been normal a couple hundred years ago).