Ask most Accordion players what a diatonic Accordion is, and most likely they will reply "the type when the note pitch changes when the bellows change". Most diatonic Accordions are "single action", however the word diatonic does not actually mean this. For me it seems that people think like that because the major characteristic of the diatonic accordion is to have two different sounds on one button when the bellows change direction, which we cannot find in chromatic accordions.

Diatonic vs Chromatic

Diatonic is a musical concept that means 'only notes from some scale'. So there is a diatonic scale of C (no sharps or flats at all), G (which includes F# but no F) and so on. This means that not only some accordions are diatonic, but other instruments, such as some types of flutes are diatonic as well. Chromatic however, includes all the sharps and flats, as well as all the naturals.

Single action vs Double action

A single action accordion, also known as a "push-pull" accordion, changes the pitch of the note according to which direction the bellows are going. For example, while holding down one key, or button, while the bellows are going out you may get a C, and when you bring the bellows in, you may play a D, depending on what type of accordion you are playing. The double action accordion doesn't change pitch when the bellows change direction.

Single action / Diatonic Accordions

This is the type of accordion most people think of as the diatonic accordion, and in fact it is the most common type of diatonic accordion. It has one or more rows of buttons in the right hand, each row consisting of the notes of a diatonic scale. In general, the scales of the rows are a 5th or a semitone apart. Some types have an additional half or whole row that consists of accidentals that are not found in the diatonic scales. The left side has bass buttons. Most common are 2, 8, or 12 basses, but diatonic accordions with more bass buttons can also be found. In general, the basses are tuned so that the tone distance between incoming and outgoing bellows is a 5th. There is another type of single action / diatonic accordion, known as the Shand accordion, for Scottish accordionist Jimmy Shand, where the right hand is three row semitone diatonic, and the left hand is the 96 bass standard double action system. Therefore when playing this accordion, when you change the bellows, the right hand changes pitch, while the left hand stays the same.

Double action / Diatonic accordions

There is also a Russian accordion, where the keyboard is in the Diatonic style, consisting of only the notes of a certain scale, but it is also double action. Therefore the pitch doesn't change when the bellows do.

Double action / Chromatic accordions

These are by far the most common type of accordion, where the keys are all a semitone apart, therefore all notes are covered, and the pitch stays the same when the bellows change direction. Both the piano accordion, and button accordion (known in Russia as the bayan) are double action / chromatic accordions.

Single action / Chromatic accordions

The prevailing type of bandoneon (well known for tango music) may be considered a Single action / Chromatic accordion. Some bandoneons are diatonic, others are chromatic, although most types change the pitch of the individual buttons when the direction of the bellows change. It seems remarkable however, that almost all the music is played while the bellows are being pulled, with the air button being used to close the bellows very quickly during a rest.

The Irish two-row button box

With this accordion, the two rows of buttons are a semitone apart, therefore every note in the chromatic scale is available. However, many people still consider this to be a diatonic accordion, since each row is a diatonic scale. It is also a single action accordion, so tunes are basically played on one row, with the other row being used for ornamentations. Therefore this instrument is still played as a single action / diatonic accordion.

The fact that most diatonic accordions are single action, and chromatic accordions are double action may be considered as coincidence, as there is nothing binding either a diatonic to be single action, or a chromatic to be double action. Indeed the word diatonic has become accepted in common use to mean single action, as this is a main characteristic of most diatonic accordions, even though the word does not mean that at all.