"Can anyone give a simple explanation of the basic different systems available on this family of squeeze boxes please? "

It will depend totally on what your box is, who made it, when it was made and how big it is. Efforts were made in Germany to standardise the two systems so later boxes are more standard.

Chemnitzers resemble anglo concertinas more closely BUT there are some which have a bass end like a melodeon. French bandoneons have the same note on both push and pull (as do the new Harry Guens bandos which are based on C or B chromatic accordion systems).

Your best bet is to sit down with your box and a piano and map your own box (it's what I did after failing to find a keyboard chart on the net). There are tutors, available from Argentina mainly, but they are mostly in Spanish and concentrate on tango.

Concerning Piazolla, if you watch film of him playing you realise that a lot of the time he "cheats" in that he'll playall the long tricky passages on the pull note only and then use the air button to push the bellows back in and start again. This simplifies things as there is almost no relationship between the position of the notes on a pull scale and a push scale. There's some good videos on Youtube.

All the best

Steve