Fallout 4 unique weapons

There are several unique weapons in Fallout 4, weapons of which only one exists in the game world. Some are found in specific locations while others are obtained as quest rewards.

Gameplay
These are different from legendary weapons which are randomly generated from a table of possible effects. Some unique weapons also have legendary effects without the normal legendary weapon prefix (e.g. assassin's, hunter's, ghoul slayer's).

Relatively few unique weapons in Fallout 4 are actually unique "base models" with unique effects or appearances in and of themselves, like the Broadsider or Deliverer; most are instead "normal" weapons that could have functionally identical duplicates randomly drop from a Legendary enemy, i.e. Kellogg's pistol is a renamed .44 pistol that is guaranteed to drop with the "Relentless" legendary effect, and the Bull barrel, standard receiver, comfort grip, and standard sights mods attached.