Be careful - there are THREE main types, all different to play, and suited to different styles of music.
English - Fully chromatic. The same note on Push & Pull, notes are arranged so that to play a scale you alternate between left and right hands.
Anglo - Just like a harmonica (or melodeon). Different note depending on whether you push or pull. Bass notes on left and treble on right Diatonic, not usually fully chromatic. They come with varying numbers of buttons, 20, 30, 33, 26 and so on.
Duet - same note on push & pull, but arranged differently to the English, in that they have Bass on the left and treble on the right. There are several different Duet systems.