Viserion and the Bear are now White Walkers, not Wights. It would be hard to confuse the two but in this case it is actually quite clear.
Viserion was killed by the Night King, but the bear's death is uncertain. They are still both White Walkers.
Reason why Viserion is a White Walker: Viserion was touched by the Night King to become a White Walker, instead of being raised by his magical hands as shown in Hardhome. This is the same cause as to regular White Walkers which are Craster's Sons whom were touched as babies to be turned into White Walkers. This now makes Viserion immune to fire, but not to Dragonglass or Valyrian steel.
Reason why the Snow Bear is a White Walker: The bear was very immune to fire, as is the case when it wasn't backing away from Thoros' flaming sword when trying to bite down on him. The bear wasn't immune to Dragonglass though, as it did take a few jabs to the shoulder and died after Jorah stabbed him with Dragonglass bladed weapons.