Brother JR is always much better at explaining this better then me, but in reality you only have two 3rd Order Franciscan Order. Third Order Regular or Third Order Secular (now known as SFO or OFS internationally.) All the groups you are probably thinking of as “Orders” are branches of either using either the original Third Order Rule or the new Secular Rule as their official Rule and maybe also using the Rule of the 1st Order. The differences come in in the adoption of their constitutions and such. Of course there can be SFO fraternities that have a more Capuchin “feel” to them, just like my fraternity probably has a Conventual “feel” to it since we meet in a Conventual friary.
If you want to be in a Franciscan Order and not be a vowed religious the only option of being in an Order that isn’t “controlled” by someone else is the SFO or SFO related group with a different name. It is officially its own order with its own rule. In order to be a lay person in any of the other groups you are a tertiary, lay, helper, or some other word that each of the respective groups refers to its lay people.
I am sure I am probably messing up some of the terminology, Brother JR is better at getting it exactly right.
The Franciscan Family has a very complicated structure compared to the other major orders.
I) The first order is friars, OFMs, Capuchin and Conventual–named for characteristics in their history. Both of these are parts of the1st order male branch of the Order, as I understand it. The Capuchins started out as a reform branch.
II) The second order is women, contemplative cloistered religious (nuns) called Poor Clares. You will almost never see one in public. This order was reformed in the 15th century so some Poor Clares are Colettine Poor Clares, the reform branch, and some are not. But they’re all nuns.
III) The third order is where it gets interesting. As I understand it, the third order was founded by St. Francis himself, as were the other orders. This 3rd order was once all non-cloistered individuals, mostly not ordained.
Some of these individuals in the 3rd order decided to live together in houses and obey as groups–this made them 3rd order regular (regular meaning not secular, not individual members). This is still going on to this day and many of the groups you see who follow the 3rd order rule but have different constitutions and practices than the SFO are in this category. The TOR and many women’s groups of Franciscan sisters are in this category. They’re third order, and part of the Franciscan order proper, but they live in convents and generally wear some kind of identifying garb, though they may not wear a full habit.
The SFO is still those who follow the 3rd order rule (now the 1978 version) but live as individuals or with their families. The secular SFO has never “split” like the 1st order and there is a lot of pressure to keep it so. All the organizational diversity in the 3rd order has always appeared around whether the members live in strict community or on their own. This is the SFO operating under CIOFS and NAFRA, the one conventionally referred to when we talk about the Secular Franciscans.
And then there are other groups that call themselves Franciscans that may use an older rule or something to identify themselves as Franciscans but they are not part of the Franciscan order proper. They are public associations of the faithful or secular institutes. BSP and the Confraternity of Penitents are examples of this type of group.
Then there are many groups, both male & female, which are really not part of the order proper, but rather are congregations of sisters or friars, with a Franciscan-like flavor. These often get confused with the Franciscan order proper. However, instead of being organized around a way of life, they’re organized around a characteristic apostolate, like teaching or medical work OR they’re organized around a particular facet of devotion, like the BVM. They may have hybrid rules, having some properties of the Franciscans and some properties of another way of life. This gets really confusing.
When talking about the Franciscans, you can describe a group by the place it holds in the 1st/2nd/3rd order structure, or outside it. You can describe a group by whether it’s regular (in a shared house) or not. You can describe it by whether it’s of diocesan right or pontifical right. You can describe it by what rule it uses or what constitutions it’s using. This is why it’s so complicated to figure out where each group belongs in the whole scheme of things. Complete descriptions are hard to come by when looking these organizations over too.
I’m not sure what might happen if a group of SFOs split off, using the same rule but different constitutions, similar to what happened with the Conventuals and the Capuchins, a sort of reform group. My feeling is that it wouldn’t be tolerated, but I’m not sure why that would be the case specifically.
The SFO has been employed through various eras of history to galvanize groups of the faithful around various types of religious practice, etc. The history is interesting. At times, it’s been treated as more of a pious group or sodality even at fairly high levels in the church, and then at other times it’s been understood as being more independent. It’s being treated independently now.
I’m not honestly sure where the Franciscan Friars & Sisters of the Immaculate fit into this picture, whether they are 3rd order regular groups or congregations with a Franciscan flavor and a modern founder. I believe the blue-garbed tertieries belong to them, as associates. I don’t think they’re part of the Order proper in any way but I could be wrong.