> US copyright does protect for "substantial similarity"
Substantial similarity refers to three different legal analyses for comparing works. In each case what the analysis is attempting to achieve is different, but in no case does it operate to prohibit similarity, per se.
The Wikipedia page points out two meanings. The first is a rule for establishing provenance. Copyright protects originality, not novelty. The difference is that if two people coincidentally create identical works, one after another, the second-in-time creator has not violated any right of the first. (Contrast with patents, which do protect novelty.) In this context, substantial similarity is a way to help establish a rebuttable presumption that the latter work is not original, but inspired by the former; it's a form of circumstantial evidence. Normally a defendant wouldn't admit outright they were knowingly inspired by another work, though they might admit this if their defense focuses on the second meaning, below. The plaintiff would also need to provide evidence of access or exposure to the earlier work to establish provenance; similarity alone isn't sufficient.
The second meaning relates to the fact that a work is composed of multiple forms and layers of expression. Not all are copyrightable, and the aggregate of copyrightable elements needs to surpass a minimum threshold of content. Substantial similarity here means a plaintiff needs to establish that there are enough copyrightable elements in common. Two works might be near identical, but not be substantially similar if they look identical merely because they're primarily composed of the same non-copyrightable expressions, regardless of provenance.
There's a third meaning, IIRC, referring to a standard for showing similarity at the pleadings stage. This often involves a superficial analysis of apparent similarity between works, but it's just a procedural rule for shutting down spurious claims as quickly as possible.