its fine, it means youve got an open diff, no locker.....
not necessarly, if its a racheting locker like a Powerlock or Locrite then you can lift the front, spin the tire and listen to it rachet.. it'll eventually catch and lock itself into place.
If it came off a stock vehicle it probably doesn't have a locker but just because you spin a tire and both don't automatically spin doesn't mean you dont have a locker in there..
Might even be a limited slip..