I would say with 95% certainty that is it, I go to a Sacred Heart Parish, which is Catholic, and have never seen a Protestant use the word "Parish" or name a Church "Sacred Heart".
A Catholic Parish is a designation of a geographical locale, established by the local Catholic diocese. It is the area that is identified as a single congregation of Catholic worshipers. A parish usually has one church in it, and one priest.
A parish
The smallest unit of the Catholic Church is the family, followed by the parish.
St Mary Church
Catholic Churches have a lot of organizations, you would have to contact your local parish to find out what theirs were.
A parish is the name for a Catholic church, it's surrounding area, and the parishioners who worship there. Chicago in and of itself is not a parish, however, it contains many Catholic churches, each of which is its own parish.
In a Catholic Church, of the person's parish
There is only one reigning pope at a time and he is the pope of the entire Catholic Church. Each parish has a pastor who is in charge of that parish only and under the same pope in the Vatican.
Espousal of our Lady Parish Church
This varies from parish to parish. However, usually the only qualification is that the sponsors just need to have been confirmed in the Catholic Church.
I believe there is at least one catholic school per 2 public schools. This is just an assumption that I've made judging by my area. Since most Catholic schools are sponsored by a local Catholic parish, they are usually located near the church of the parish that sponsors them and usually bear the same name as the parish church.