Not that I'd expect a show like this to even vaguely adhere to even basic astrophysics, but lets just say for the sake of argument it did: for a planet to be that badly hit by the debris field of another exploding planet and in any kind of sensible time frame, it would pretty much have to be in the same system and almost certainly withing Rao's habitable zone.Heck, think of India and Pakistan, or Britain and Ireland and Scotland back in the day. You can have hostilities and cultural differences and still have overlapping roots and linguistics. Krypton and Daxam have clearly had enough contact with each other to generate plenty of bad blood, which makes me figure they're probably related somehow. Family feuds are often the most deep-rooted.
So yeah, odds are they are related, most likely with one being the former colony of the other from *way* back.