Why are the Benedictines and Dominicans two groups? They have a different "spirituality".
The FSSP is most like diocesan clergy. The ICKSP is most like canons; they have a more extensive rule and are a little more independent of the diocese. They generally arrange long-term leases and often restore buildings.
Also, the ICKSP was a separate entity with no connection to the FSSP or SSPX. The FSSP were originally SSPX priests who did agree with the consecration of bishops, but otherwise agreed with SSPX positions.
The FSSP was compromised when they were forced to agree that priests could be bi-ritual with the N.O. This was pushed by a few priests in Europe. Even 20+ years ago, priests who left the SSPX for the FSSP had to sign a docuмent agreeing to the "valitudinem" (health, wellness) of the N.O., quite a bit more than +ABL agreeing to the "validitatem". The ICKSP, at least to my knowledge, has not compromised in those ways.