Why it matters when you are writing
Ibid. only ever refers to the note directly preceding it. That makes it fragile during revision: move a paragraph, insert a note, or let a co-author drop a citation in between, and every following ibid. now points at the wrong source without any visible sign that anything broke. This is the practical reason the seventeenth edition of Chicago recommends the shortened form — author surname, short title, page — over ibid. in most cases.
When you do use it, capitalize it at the start of a note and add a locator only when the page changes. “Ibid.” alone means the same source and the same page; “Ibid., 91” means the same source at a different page. It does not carry across a chapter break, and most publishers will not let it stand as the first note of a chapter.
Author–date systems have no equivalent and need none, because a repeated citation is already only a surname and a year. If you find yourself wanting an ibid. in an APA or Harvard paper, what you actually want is to name the author once in the sentence and let the reader carry the attribution forward.