Well, the differences between all the many Franciscan orders could be the subject of a lifetime of study, I suspect. But the “big 3”, OFM, OFM Conv (Conventual Franciscan), and OFM Cap (Cappuchin Franciscan), I would summarise as follows (and I invite comments and corrections on this, as it is not an area I claim to understand completely):
OFM: ‘Ordinary Franciscans’ (if there could be such a thing!). These are all those Franciscans that were grouped together by the Leonine Union (after Pope Leo XIII, who joined together a number of Franciscan groups).
OFM Conv: ‘Conventual Franciscans’ originally separated from the earlier branches by adopting a more ‘conventual’ (that is, convent-based) lifestyle, as opposed to the more rural, traveling style of the original Franciscans. Being more solidly established where they were allowed them to adopt certain ministries more effectively than the older OFM. St. Maximilian Kolbe was an OFM Conv.
OFM Cap: ‘Cappuchin Franciscans’ took their ‘Cappuchin’ habits from the Camaldolese, one of the strictest cloistered monastic orders in the church. Some of their spirituality was influenced by the Camaldolese, who sheltered their founder, the reformer Matteo da Bascio. Generally they are a reform of the Franciscan order in later times, designed to bring a more strict return to their founders principles. As such they might be considered analogous to the Cistercians vis-a-vis the Benedictines, or the OCD vis-a-vis O.Carm.
Another point of view (read: gross generalisation!) would be to say that the OFM view themselves as more faithful to Francis’ original vision than the OFM Conv, while the OFM Cap see themselves as more faithful to that vision than the OFM. (Although I’m sure today all would acknowledge that all Franciscans live truly and fully the Franciscan vocation, in their own way!)
I should also mention:
TOR: Third order regular, are most easily distinguished from the above by being a lay order (not priests), with an active apostolate. They are thus conceptually like a midway point between the SFO and OFM: like the OFM, they take religious vows and live a consecrated life, but unlike them and like the SFO, their life is lived more engaged in the world, and not as priests.
There are WAY more Franciscan groups than just these, but to my understanding these are the more fundamental ‘archetypes’, again I welcome correction to any of my impressions. Also Br. JR who often posts here is “OSF”, I have no idea what that refers to, and would welcome further knowledge on his branch of the Franciscan family!