That’s pretty accurate. They are considered a private school whereas Chatard, Ritter, Roncalli and Scecina are Catholic Archdiocese schools (ie. funded in part by and beholden to the Indianapolis Catholic Archdiocese).
As to the question above regarding vocational classes, I’m pretty confident that they don’t have “shop” class, etc. but does any single high school have that these days? Serious question. One of my kids took a cooking class at one time I believe.
Which leads me to a story. I tried to sign up for a Home Ec class back in the day because I wanted to learn to cook and was called into the Office for it. It was literally scandalous. They never let me take the class as it turned out. I can barely warm an egg these days.