Other then 2nd Order Franciscan, all the different groups don’t really vary their ministries based on which order they are, they vary their ministries usually based on location, region, friary, etc.
There is a branch of 1st Order friars called the Custos of the Holy Land. Their primary ministry is to both the Shrine of the Holy Land and the people of the Holy Land.
Some groups tend to assist in schools, some in college (i.e the Greyfriars), some have Pro-life ministries.
The 2nd Order Franciscans tend to be cloistered nuns so you don’t tend to see them a lot.
The main groups are 1st Order - OFM, OFM Capuchin, and OFM Conventual.
2nd Order - Poor Clares and other derivations with Clare in the title
3rd Order - Secular Franciscan Order and Third Order Regular (Many Franciscan groups without OFM in their title tend to fall in this category.)
All follow St. Francis’ and St. Clare’s ideals. All of them do it in different ways, all of them as long as they are under the auspices of the Catholic Church are part of the same family.