Joe,
The other schools are diocesan schools, which means they are the creations of the archdiocese, with the principals appointed by an archdiocesan official, with the teachers under the same contract, the tuition established by the archdiocese, their buildings and land owned by the archdiocese, etc The Prep and LaSalle are both Catholic schools, but they have their own governance, own their own land and buildings, negotiate separately with their teachers, decide on their own tuition rates, etc. They're founding members of the Catholic League and have, at least until very recently, drawn most of their students from archdiocesan elementary schools. (When I was a student at SJP every student was from a Catholic family. Now a number of students, and not just athletes, are not. It's a different world.)
The bottom line in this discussion is that they have financial autonomy while the other league schools do not. Their tuition rates are, last I checked, about four times what the other schools charge. They each have programs to help families who can't afford the full tuition--as do the other league schools, but it's obviously on a different scale. Finally, both LaSalle and SJP are more academically selective and demanding than the other schools, though how much more selective and demanding is sometimes disputed.