OK thank you, you've been very helpful. I was just saying in my last update that I don't think what you've suggested will work for the MacBook I've been trying to use (the 2019 one), as the instructions seem to say that you need a thunderbolt cable - which led to my question about the adapter.
I do now have a silicon MB (but this only arrived today) that the USB-C to A cable might work on, but that only arrived today. I did already try this cable with the 2019 MBA, and it couldn't recognise the old MBP disk in target disk mode. This could either be because the disk is toast, or it could be be cause I need a thunderbolt cable.
Anyway, do you know the answer to my original question, which is how can I connect the apple thunderbolt adapter between my 2015 MBP and the 2019 MBA - I am coming to my own conclusion that I think I must need another cable (a thunderbolt 2 cable) otherwise I can't see how it could possibly work.. It would be most helpful if the apple website actually said that! Saying it's bidirectional, implies to me that it should just work in both directions way without anything additional. Cables are an absolute minefield, so it would help if things like this were explained in clear and comprehensive detail!