Very cool, if true

Yes, sorry. When most people in the UK they are referring to a "Doner Kebab", which is the shaved meat thing (served in a Pita pocket), but it is _absolutely_ appropriate to also be referring to a shish kebab, which (as you say) is the chunk of "meat on skewers".

Meanwhile I've been confused by the description I've seen online of Shawarma. Clearly it's the meat bit, and putting it in pita makes it a "Pita Bread Sandwich" in the USA.

I think I've learned something!