No, those aren't the same thing at all, and this is made obvious by the examples they give on that page. "Identifying information" refers to revealing the true

No, those aren't the same thing at all, and this is made obvious by the examples they give on that page. "Identifying information" refers to revealing the true identity of a pseudonymous user on the site (e.g., violentacrez), or a person who has no previous association with the site (e.g., Sunil Tripathi). In these cases the perpetrators used information that was known only to them, or that the "public" had no easy access to, or that the "public" didn't even know existed until the perpetrators brought it to their attention.