[tsilva]

> Definition and equality are really the same thing. [...] So the only difference is [...].

An interesting way of justifying how two things are really the same thing, that is, by acknowledging their difference.

The point is that the pointed ambiguity (the difference) can be quite significant, and these become apparent when studying these sentences in a formal logic. Hence, the significance of the ambiguity.

This (and the article under discussion) just echoes the idea that mathematical sentences and proofs are considered "rigorous" but "informal", where "formal" is the domain of logic.