The part I don't completely understand is why one some tutorials say to use regular vinegar and others apple cider vinegar or even balsamic vinegar.
What most guides don't simply spell out in plain English is this process is actually a chemical reaction in which you're making iron acetate.
The iron acetate then reacts with the tannins in the wood, which forms iron tannate, a black metallic salt: hence the very dark colour in some oak (high in tannins) and the slight greying you usually get in softwoods (very low in tannins).
So anyway, the reason to prefer one vinegar over another is simply to do with the acetic acid content. Higher acetic acid level = more iron acetate formed. With a stronger vinegar you get a stronger solution of iron acetate and this give a more pronounced reaction in the wood, and faster.
Regardless of the name they all involve at a minimum rust and vinegar.
In reality you just need iron and vinegar. Rusty metal is no more or less desirable here, as seen by the most common method of forming this 'dye' which uses steel wool.
However there is a bonus if you do use rusty nails, as this will do two things simultaneously: it will clean the rust from your nails as well as forming the iron acetate solution :-)
I should add here that if you're specifically looking to do ebonising this alone is not a reliable way to get there. Wood, even oak, is often not quite high enough in tannins to make a good black colour and it can vary even from piece to piece in the same lot of wood, so you could end up with one grey board within an otherwise black piece.
There are various chemical means to achieve a more reliable black, e.g. by introducing tannic acid to the wood, or with sulphuric acid and a heat gun, but the simplest (and safest!) method is just to paint the wood with Indian ink.