Don't forget the main difference in accordians, chromatic or diatonic.

A piano accordian plays like, well, a piano. Bellows pushed or pulled doesn't change the note. Sharps and flats are available.

Buttonboxes generally have a different note on the push and the pull. (4 buttons give you an 8 note scale) Bass buttons are chords. Each row of treble is a specific key.

Then there's the concertina. Octagon shape or square. I think these have treble notes that alternate from right hand to left.

My favorite is my little 2 row Hohner from Germany. Light weight and easy to learn. Very versatile for Folk, tango, Cajun, Eastern Europe, etc. music. Mine was available in the Sears catalog in 1957 for about $75. Any my Dad couldn't believe they had gone up that much in price since he bought his!