Crane Drive:"I was always given to understand that the fundamental difference between concertinas and other 'squeezeboxes' is that on a concertina the movement of the buttons is in the same direction as the movement of the bellows, whereas on melodeons and accordions the button movement is at right-angles to the direction of bellows movement"

RE:Such a definition may hold to some part but what is the use of it?
There are typical big squeezeboxes looking like common "accordions" but with the buttons arranged "concertina-wise".
Another suggested definition is based on 'one or more notes/button'
Accordion,Akkordeon,Accordeon...indicates something with *chords* being a basic feature but there are "accordions" with "free bass" that fall out.

To make a definition or classification useful it must better have some universal fundament of organologic separation otherwise we get numerous exceptions or "hybrids".
The best I can come up with classifying "bellows-driven free reed instruments " is the principle for pumping air.We already have got various *blown* free reed instruments like harmonicas with or without keys. For the *pumped* ones I suggest the following

x. bellowsdriven free reed instruments

x.1 Stationary = (resting on ground or table while being played)
x.1.1 organs, harmoniums with pedals
x.1.2 Indian harmonium, pumped with one arm, "keyed" with the other

x.2 Portable = ( carried while being played)= Squeezeboxes
x.2.1 Accordions = (assymmetrical construction)bellows worked with one arm
x.2.2 Concertinas = (symmetrical construction) bellows worked by either arm or both arms