This bass system is called Stradella and is the most common accordion bass system in the world.
The buttons in the bass rows produce single notes (several reeds in different octaves may be combined, however). There’s only one octave available using a given registration – several keys produces the same sound.
The buttons in the chord rows combine several notes into a chord. The same reeds are used for different chords. 7th and dim chords often use only three notes even though four are needed in theory.
Other chords may be formed using left hand chord combining.
Free Bass systems are an alternative to the Stradella system. They are not common and are used mostly by professional players.
Basically you have only four chord types but other types are possible using combinations of keys. Intermediate or advanced players compensates this using right hand chords and/or bass runs instead.
The number of buttons is 120 (20*6) on a full size instrument. You really don’t need more than 72 (12*6) in order to play all bass notes and corresponding chords. Using only 72 basses, however, is more demanding since you have to do unnecessarily long jumps in certain keys or when doing bass runs.