Reading is good, but for someone as unsure of everything as you seem to be, I think you should do everything you can to try one or more different types of box before you buy one. Or be sure exactly what type of music you want to play, and be guided by what most people playing that type of music use.
The main question I have is, do all button accordions play 2 notes on one button depending on whether you push or pull?
For most button accordions used in folk music, yes. The correct term for this is a “single-action” accordion. But there are also chromatic button accordions - generally much bigger instruments, similar to piano accordions, which are “double-action” - play the same note on push and pull. These are often called continental chromatic button accordions.
And what is the difference between chromatic and diatonic accordions?
Strictly speaking, a diatonic accordion can play only the notes of a single major scale. For example, a one-row accordion in the key of C can play only the white notes on the piano and nothing else. Instruments like this are always single-action (different note on push and pull). They are like a basic harmonica, but with bellows.
A chromatic accordion can play every note in the Western music system - all the white and the black notes on a piano. Generally that means a piano accordion or a continental chromatic button accordion.
That’s the simple version. Things get a little more complicated, because common diatonic accordion systems have two or three rows of buttons, giving more possibilities. And systems commonly used by Irish musicians have two rows a semitone apart, which allows all of the notes of the scale to be played - meaning that they are chromatic as well as diatonic. (But less versatile than the true chromatic types mentioned above.)
I have been looking at both button and piano accordions. Is there one you would say is easier to learn on?
Hard to say. Piano accordion might be easier initially if you already play piano. Some people take to diatonic systems like ducks to water, and some just can’t get their heads around them.
Try both. And as I said, decide what music you want to be able to play. If you want to be able to play anything, including jazz and classical, for instance, better go for a piano accordion or even better IMO one of the continental chromatic systems.
If you want to play folk music only, a diatonic system has some big advantages - smaller, cheaper, lighter, and allow you to play with great punch more easily. I and others can probably give more detailed suggestions if you tell us what you are aiming to play.
Steve
and quicker to get going on. You can find lots of discussion of the relative merits of these two systems here and elsewhere. Whatever I may say about the advantages of C#/D, there is a total absence of tutor books and DVDs for this system, but quite a lot available for B/C.