To expand on this point, one resolution to the Ship of Theseus problem is that the point at which the ship stops being the "same" ship depends on how you are going to define "same." "Same" could mean different things depending on what you are trying to do, so this isn't just an it's-just-semantics cop-out. In particular, to borrow something Ravi Vakil once said, a definition is worthless unless it has a use (which in his case, as a mathematician, if it can be used to uncover and prove a theorem). This is what I have in mind: I do not think it is worthwhile to worry about "the true length of a Unicode string" unless there is something you could do if only you could compute it, and I've been trying to think of something but have come up short.

Speaking of equality: in a lecture about logic I once gave, I asked the students whether {1,2} and {1,2} were the same. In a very real sense, they are different because I drew them (or typed them) in different places and slightly differently -- I promise I typed the second {1,2} with different fingers. But, through the lens of same-means-same-elements, they are the same. That is a warmup for {1,2} vs {1,1,2}, and {1,2} vs {n : n is a natural number and 1 <= n <= 2}.

(There's also kind of a joke about how my set of natural numbers might be red and your set of natural numbers might be blue, but the theory of sets doesn't care about the difference.)