D/G or G/C melodeon: what's the difference?
They're the same instrument in two sizes of key. A G/C has exactly the layout of a D/G, moved down a fifth. What changes is which keys fall easily under your fingers, how low the box goes, and the bass.
The same pattern, a fifth apart
On a D/G the outside row is in D and the inside row in G. On a G/C the outside row is in G and the inside row in C. Button for button, every note on a G/C is a fifth below the same button on a D/G, accidentals included on Hohner-pattern boxes, so tab written for one plays the same tune on the other, a fifth lower.
That puts the two boxes in different places. A D/G runs from A3 to B6, and a G/C from D3 to E6.
The keys each one plays
Without touching the accidental buttons, a D/G has a complete octave in G and D major and E and B minor. A G/C has C and G major and A and E minor.
That matters when you play with other people. Most English and Irish session tunes are in D and G and their related minors and modes, and a D/G handles D and G comfortably. A G/C is at home in G and C instead. The pages on D/G keys and G/C keys check every key one by one.
Where each is played
Musical Traditions puts it simply: in England players mostly use D/G and play in the lower octave, while in continental Europe they prefer G/C and play mainly in the upper octave. The melodeon players' FAQ on Reddit says the same of English folk music, and adds that G/C is preferred in France and parts of North and South America.
Neither is a rule. People play English tunes on G/C and French tunes on D/G; it changes which octave the tune sits in, not whether it works.
The bass side
The eight basses move down a fifth with the treble. On a D/G the outer row gives D and G on the push and A and D on the pull, with B, E minor and C on the inner row. On a G/C the outer row gives G and C on the push and D and G on the pull, with E, A minor and F on the inner row. The D/G and G/C charts list them button by button.
So which?
Go by the music and the people. If you'll mostly play English tunes, or play with fiddles and whistles in D and G, a D/G is the usual box. If you're drawn to French and continental dances, or want a lower sound, a G/C is worth a look. If there's a session or a teacher near you, find out what they play: it's much easier to learn alongside someone with the same box.