How a B/C button accordion works
A B/C box looks like a melodeon and works like one, a different note on the push and the pull. The difference is the tuning of the rows: B and C are a semitone apart, so between them they hold nearly every note.
Two rows, a semitone apart
The outside row is in B and has eleven buttons; the inside row is in C and has ten. On a D/G the rows are a fourth apart and share most of their notes. On a B/C they share almost none, so the notes one row lacks are mostly on the other.
The result is close to chromatic. Over the whole treble side, from D♯ below middle C to the F♯ just over three octaves up, only three notes are missing: F3, D6 and F6. There are no accidental buttons because there's no need for them.
Playing in D
The price is that no row holds the common session keys on its own. D major needs F♯ and C♯ from the B row and D and G from the C row, so its scale has to cross between them. This is D major from the D above middle C, with the fewest changes of bellows:
That's two changes of bellows and four moves between rows.
B/C and C♯/D
A C♯/D box has the same layout a whole tone higher, the C♯ row outside and the D row inside. Writing in 2003, Musical Traditions says Irish players used one-row boxes and D/G or similar two-rows until around 1950, when many moved to B/C, and that a good number were then moving to C♯/D. Semitone boxes were in use before that: Joe Derrane moved to a D/C♯ around 1947. Today B/C is the most widely played system in Irish music.
Because the layout is the same, tab carries straight over, but the tune moves with it: a tune tabbed in D for a B/C comes out in E on a C♯/D. To play it in D on a C♯/D, it needs fingering afresh.
The bass side
A 21-key B/C usually has eight basses. The traditional set has G and C on the push of the outer row with D and G on the pull, then E with A and C with F on the inner row. Some makers vary it; the B/C chart has the details.