Also, some weapon types, such as whips and fist weapons are never procedurally generated and so are always Unique Weapons.
Not all Unique Weapons were conceived this way - some are special drops from Bosses and weapons crafted by a player have fixed stats.
Many Unique Weapons exist to meet the requirements of a Solarium-tier Pre-Order backer pledge, where the backer was entitled to design a weapon to be included in the final release. The tag 'Unique Weapon' is also given in-game to weapons that do not fit a typical weapon type (such as Assault Rifle or Broadsword) but there are many of these more typical weapons that are also Unique but do not carry the tag due to engine limitations. Unique Weapons are specially designed weapons that are not procedurally generated, but have a fixed design - they will always have the same appearance, damage, fire speed, weapon tier and capabilities whenever they are found.