Yep, We'd call a C/g our 'd' concertina, a Csharp/Gsharp an 'Eb' concertina and a Bb/F a 'C' concertina etc. suppose its the association with other instruments (a 'D' flute/tin whistle etc.) the main key we're playing in.
An for 20 button, I have never come across a 20 button in a session/ concert here ever. Maybe it would be a new trend to start though.