Others are a distinct human-like species who are known to dwell the cold North beyond the wall. Unlike Humans who are warm blooded, Others despise everything with warm blood in their veins. They are also called the White Walkers.
Others first appeared 8,000 years ago during the Long Night but they were defeated by Night's Watch and the Last Hero during the battle for Dawn. Afterwards, a Lord Commander of Night's Watch (Night's King) was found to have married one of the Others which means that Others were never truly destroyed and they still existed. After defeat of that Lord Commander, Others disappeared from annals of History and reappeared approximately 8300 years later during King Robert Baratheon's reign.
Others are living creatures as confirmed by the author:
The Others are not dead. They are strange, beautiful… think, oh… the
Sidhe made of ice, something like that… a different sort of life…
inhuman, elegant, dangerous.
Others wield swords made of some special sort if Ice as described by the author:
Ice. But not like regular old ice. The Others can do things with ice
that we can't imagine and make substances of it.
Others leave no footprints on snow. Others can't be killed by common steel weapons or fire but fire still frustrates them. As Melisandre said:
Necromancy animates these wights, yet they are still only dead flesh.
Steel and fire will serve for them. The ones you call the Others are
Others are known to be vulnerable to Dragon-glass weapons. Others can reanimate dead animals and humans. They can ride dead animals and use dead humans as their soldiers.
Others have shining blue eyes like stars and they are skilled swordsmen and very quick. Others are known to communicate with each other speaking a harsh sounding language which sounds like cracking of ice.
Wights are corpses that are reanimated by Others using some undisclosed super-power.
They usually retain the appearence their corpses have at time of their reanimation but their eyes turn blue like their masters and their hands and feet turn black due to pooled blood at extremities of the body.
Wights are very strong but they are also very slow and clumsy. Wights can pretend to be dead successfully. However it is unclear whether they do it themselves or are controlled remotely by their masters when doing that. Wights can be stopped by total dismemberment or by setting them on fire. After destruction, their eyes return to their original state instead of the bright blue color.
While Wights do not retain their personality and memories of their lives but they seem to remember some of it. It is not confirmed if Wights can communicate with each other or talk. Wights also appear to use their weapons as evident from Death of Ser Jeremy Rykker but it appears that wights usually prefer brute strength instead of weapons in battle.
It is also unclear if Wights can speak because Jon wanted to know if they can. Since there is no reference to Wights communicating, we will assume they can't speak. Also because Wights can be destroyed by dismembering their parts, Dragon-glass can also serve in this regard.
So to sum it up:
║ 𝐏𝐫𝐨𝐩𝐞𝐫𝐭𝐲 ║ 𝐎𝐭𝐡𝐞𝐫 ║ 𝐖𝐢𝐠𝐡𝐭 ║
║ Is Dead ║ X ║ ✓ ║
║ Can create substances from ice ║ ✓ ║ X ║
║ Wields Ice Swords ║ ✓ ║ X ║
║ Leaves footprints on Snow ║ X ║ ✓ ║
║ Can be killed by steel and fire ║ X ║ ✓ ║
║ Can be killed by Dragonglass ║ ✓ ║ ✓ ║
║ Can reanimate the dead ║ ✓ ║ X ║
║ Is Quick ║ ✓ ║ X ║
║ Has blue Eyes ║ ✓ ║ ✓ ║
║ Can speak ║ ✓ ║ X ║
║ Has black feet and hands ║ X ║ ✓ ║
║ Is a Thrall ║ X ║ ✓ ║
║ Wears magical armour ║ ✓ ║ X ║
Also See What are the origins of White Walkers?