It belonged to Odin. He bequeathed it to Thor later.
it wasn't a kings weapon though
there is no "kings weapon" that was something made up for the movie.
stormbreaker in the comics isn't even an axe it's a hammer of lesser power then mjolnir
A "Kings weapon" is an old smithy's term for a weapon's quality (such high quality it should only be wielded by/can only be afforded by royalty) reference The Magicians and the dagger used to slay The Beast was called a Kings weapon.
Mjolnir was NOT used by Odin but was commissioned by Odin specifically for Thor.
Stormbreaker in the comics has EXACTLY the same enchantments and powers as Mjolnir as decreed by Odin himself. The only difference was the enchantment used to turn Thor into Donald Blake was removed from Mjolnir and put on Stormbreaker to allow Beta Ray Bill to change from his cyborg form.