Developer experiences from the trenches
PCG uniqueness scale. Higher is more interesting.
The asset is a direct copy. If an asset is not perceivably different than the one next to it, it is effectively not unique, and is a direct copy.
The asset is visibly distinguishable from another of the same class but is otherwise not special. If an asset is not the same as the one next to it, it is locally unique. It must be perceivably different than the one next to it, but if there are a hundred variations, none of the variations are special. This is the lowest form of uniqueness: it is not a copy, but variants do not provoke further classification by the user. Perlin noise textures are an example of this. Many people believe that this is the true limit of procedural content uniqueness. Not even close.
The asset violates a sense of classification if placed in another area. If an asset would be illogical to a user to place in another area or seemingly makes sense only in the areas where it is placed, it is divisionally unique. Terrain generators that make use of biomes to generate palm trees in tropical areas are divisionally unique.
The asset is notably unique regardless of, or due to, spatial separation. The asset stands out from its surroundings due to properties which are unique from others in its perceived class. It is parametrically unique. A single tree which is larger than all the rest, burned and charred and on the highest hill is an example of this.
The asset has unique properties which simply enforce an entirely different classification by the end user. This may be in spite of a single set of algorithms generating each property under the hood. It is unique by genus. A watermelon in a basket of apples qualifies as being unique by genus.
The asset cannot exist in the same world as another asset. There is no logical way for two assets to exist in the same world. They are represented in such a different manner that there is no opportunity for them to reasonably coexist.